BuyFind*arrow_forward*

7th Edition

James Stewart + 2 others

Publisher: Brooks Cole

ISBN: 9781305071759

Chapter 11.4, Problem 26E

Textbook Problem

1 views

**Graphing Shifted Hyperbolas** An equation of a hyperbola is given. **(a)** Find the center, vertices, foci, and asymptotes of the hyperbola. **(b)** Sketch a graph showing the hyperbola and its asymptotes.

**26.**

(a)

To determine

**To find:** The center, vertices, foci and asymptotes of the hyperbola

**Definition used:**

**Definition 1:**

“The equation of the shifted hyperbola with center as
*x*-axis) axis as transverse axis is

**Definition 2:**

“The equation of the hyperbola with center at the origin, vertices

**Definition 3:**

“The equation of the asymptotes of the hyperbola

**Definition 4:**

“If

**Calculation:**

The given equation of conic is

Now, by the definition 1, the equation (1) is a shifted hyperbola

That is, equation

Therefore, first find the center, vertices and foci of the hyperbola
*x*-coordinates remains same and *y*-coordinates by 2 units downward.

Compare the equation (2) with the hyperbola

Clearly,

By definition 2,

Now, find the center, vertices and foci of the unshifted hyperbola represented by equation (2) and then obtain the respective values for the shifted hyperbola represented by equation (1) as follows in Table 1

(b)

To determine

**To sketch:** The graph of the hyperbola

Precalculus: Mathematics for Calculus (Standalone Book)

Show all chapter solutions

Ch. 11.1 - A parabola is the set of all points in the plane...Ch. 11.1 - The graph of the equation x2 = 4py is a parabola...Ch. 11.1 - The graph of the equation y2 = 4px is a parabola...Ch. 11.1 - Label the focus, directrix, and vertex on the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...

Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Graphing Parabolas Use a graphing device to graph...Ch. 11.1 - Graphing Parabolas Use a graphing device to graph...Ch. 11.1 - Graphing Parabolas Use a graphing device to graph...Ch. 11.1 - Graphing Parabolas Use a graphing device to graph...Ch. 11.1 - Graphing Parabolas Use a graphing device to graph...Ch. 11.1 - Graphing Parabolas Use a graphing device to graph...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Families of Parabolas (a) Find equations for the...Ch. 11.1 - Families of Parabolas (a) Find equations for the...Ch. 11.1 - Parabolic Reflector A lamp with a parabolic...Ch. 11.1 - Satellite Dish A reflector for a satellite dish is...Ch. 11.1 - Suspension Bridge In a suspension bridge the shape...Ch. 11.1 - Reflecting Telescope The Hale telescope at the...Ch. 11.1 - DISCUSS WRITE: Parabolas in the Real World...Ch. 11.1 - DISCUSS: Light Cone from a Flashlight A flashlight...Ch. 11.2 - An ellipse is the set of all points in the plane...Ch. 11.2 - The graph of the equation x2a2+y2b2=1 with a b 0...Ch. 11.2 - The graph of the equation x2b2+y2a2=1 with a b 0...Ch. 11.2 - Label the vertices and foci on the graphs given...Ch. 11.2 - Graphs of Ellipses Match the equation with the...Ch. 11.2 - Graphs of Ellipses Match the equation with the...Ch. 11.2 - Graphs of Ellipses Match the equation with the...Ch. 11.2 - Graphs of Ellipses Match the equation with the...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Graphing Ellipses Use a graphing device to graph...Ch. 11.2 - Graphing Ellipses Use a graphing device to graph...Ch. 11.2 - Graphing Ellipses Use a graphing device to graph...Ch. 11.2 - Graphing Ellipses Use a graphing device to graph...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Intersecting Ellipses Find the intersection points...Ch. 11.2 - Intersecting Ellipses Find the intersection points...Ch. 11.2 - Intersecting Ellipses Find the intersection points...Ch. 11.2 - Intersecting Ellipses Find the intersection points...Ch. 11.2 - Ancillary Circle The ancillary circle of an...Ch. 11.2 - Family of Ellipses (a) Use a graphing device to...Ch. 11.2 - Family of Ellipses If k 0, the following equation...Ch. 11.2 - How Wide Is an Ellipse at a Focus? A latus rectum...Ch. 11.2 - Perihelion and Aphelion The planets move around...Ch. 11.2 - The Orbit of Pluto With an eccentricity of 0.25,...Ch. 11.2 - Lunar Orbit For an object in an elliptical orbit...Ch. 11.2 - Plywood Ellipse A carpenter wishes to construct an...Ch. 11.2 - Sunburst Window A sunburst window above a doorway...Ch. 11.2 - DISCUSS: Drawing an Ellipse on a Blackboard Try...Ch. 11.2 - DISCUSS: Light Cone from a Flashlight A flashlight...Ch. 11.2 - DISCUSS: Is It an Ellipse? A piece of paper is...Ch. 11.3 - A hyperbola is the set of all points in the plane...Ch. 11.3 - The graph of the equation x2a2y2b2=1 with a 0, b ...Ch. 11.3 - The graph of the equation y2a2x2b2=1 with a 0, b ...Ch. 11.3 - Label the vertices, foci, and asymptotes on the...Ch. 11.3 - Graphs of Hyperbolas Match the equation with the...Ch. 11.3 - Graphs of Hyperbolas Match the equation with the...Ch. 11.3 - Graphs of Hyperbolas Match the equation with the...Ch. 11.3 - Graphs of Hyperbolas Match the equation with the...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Graphing Hyperbolas Use a graphing device to graph...Ch. 11.3 - Graphing Hyperbolas Use a graphing device to graph...Ch. 11.3 - Graphing Hyperbolas Use a graphing device to graph...Ch. 11.3 - Graphing Hyperbolas Use a graphing device to graph...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Perpendicular Asymptotes (a) Show that the...Ch. 11.3 - Conjugate Hyperbolas The hyperbolas...Ch. 11.3 - Equation of a Hyperbola In the derivation of the...Ch. 11.3 - Verifying a Geometric Property of a Hyperbola (a)...Ch. 11.3 - Confocal Hyperbolas Hyperbolas are called confocal...Ch. 11.3 - Navigation In the figure on the next page, the...Ch. 11.3 - Comet Trajectories Some comets, such as Halleys...Ch. 11.3 - Ripples in Pool Two stones are dropped...Ch. 11.3 - DISCUSS WRITE: Hyperbolas in the Real World...Ch. 11.3 - DISCUSS: Light from a Lamp The light from a lamp...Ch. 11.4 - Suppose we want to graph an equation in x and y....Ch. 11.4 - The graphs of x2 = 12y and (x 3)2 = 12(y 1) are...Ch. 11.4 - The graphs of x252+y242=1 and (x3)252=(y1)242=1...Ch. 11.4 - The graphs of x242y232=1 and (x3)242(y1)232=1 are...Ch. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Use a graphing device to...Ch. 11.4 - Graphing Shifted Conics Use a graphing device to...Ch. 11.4 - Graphing Shifted Conics Use a graphing device to...Ch. 11.4 - Graphing Shifted Conics Use a graphing device to...Ch. 11.4 - Degenerate Conic Determine what the value of F...Ch. 11.4 - Common Focus and Vertex Find an equation for the...Ch. 11.4 - Confocal Parabolas This exercise deals with...Ch. 11.4 - Path of a Cannonball A cannon fires a cannonball...Ch. 11.4 - Orbit of a Satellite A satellite is in an...Ch. 11.4 - DISCUSS: A Family of Confocal Conics Conics that...Ch. 11.5 - Suppose the x- and y-axes are rotated through an...Ch. 11.5 - Consider the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 (a) In...Ch. 11.5 - Rotation of Axes Determine the XY-coordinates of...Ch. 11.5 - Rotation of Axes Determine the XY-coordinates of...Ch. 11.5 - Rotation of Axes Determine the XY-coordinates of...Ch. 11.5 - Rotation of Axes Determine the XY-coordinates of...Ch. 11.5 - Rotation of Axes Determine the XY-coordinates of...Ch. 11.5 - Rotation of Axes Determine the XY-coordinates of...Ch. 11.5 - Finding the Equation for a Rotated Conic Determine...Ch. 11.5 - Finding the Equation for a Rotated Conic Determine...Ch. 11.5 - Finding the Equation for a Rotated Conic Determine...Ch. 11.5 - Finding the Equation for a Rotated Conic Determine...Ch. 11.5 - Finding the Equation for a Rotated Conic Determine...Ch. 11.5 - Finding the Equation for a Rotated Conic Determine...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Identifying a Conic from Its Discriminant (a) Use...Ch. 11.5 - Identifying a Conic from Its Discriminant (a) Use...Ch. 11.5 - Identifying a Conic from Its Discriminant (a) Use...Ch. 11.5 - Identifying a Conic from Its Discriminant (a) Use...Ch. 11.5 - Identifying a Hyperbola Using Rotation of Axes (a)...Ch. 11.5 - Identifying a Parabola Using Rotation of Axes (a)...Ch. 11.5 - Rotation of Axes Formulas Solve the equations...Ch. 11.5 - Graphing an Equation Using Rotation of Axes Show...Ch. 11.5 - PROVE: Matrix Form of Rotation of Axes Formulas...Ch. 11.5 - PROVE: Algebraic Invariants A quantity is...Ch. 11.5 - DISCOVER PROVE: Geometric Invariants Do you...Ch. 11.6 - All conics can be described geometrically by using...Ch. 11.6 - The polar equation of a conic with eccentricity e...Ch. 11.6 - Finding a Polar Equation for a Conic Write a polar...Ch. 11.6 - Finding a Polar Equation for a Conic Write a polar...Ch. 11.6 - Finding a Polar Equation for a Conic Write a polar...Ch. 11.6 - Finding a Polar Equation for a Conic Write a polar...Ch. 11.6 - Finding a Polar Equation for a Conic Write a polar...Ch. 11.6 - Finding a Polar Equation for a Conic Write a polar...Ch. 11.6 - Finding a Polar Equation for a Conic Write a polar...Ch. 11.6 - Finding a Polar Equation for a Conic Write a polar...Ch. 11.6 - Graphs of Polar Equations of Conics Match the...Ch. 11.6 - Graphs of Polar Equations of Conics Match the...Ch. 11.6 - Graphs of Polar Equations of Conics Match the...Ch. 11.6 - Graphs of Polar Equations of Conics Match the...Ch. 11.6 - Graphs of Polar Equations of Conics Match the...Ch. 11.6 - Graphs of Polar Equations of Conics Match the...Ch. 11.6 - Polar Equation for a Parabola A polar equation of...Ch. 11.6 - Polar Equation for a Parabola A polar equation of...Ch. 11.6 - Polar Equation for a Parabola A polar equation of...Ch. 11.6 - Polar Equation for a Parabola A polar equation of...Ch. 11.6 - Polar Equation for an Ellipse A polar equation of...Ch. 11.6 - Polar Equation for an Ellipse A polar equation of...Ch. 11.6 - Polar Equation for an Ellipse A polar equation of...Ch. 11.6 - Polar Equation for an Ellipse A polar equation of...Ch. 11.6 - Polar Equation for a Hyperbola A polar equation of...Ch. 11.6 - Polar Equation for a Hyperbola A polar equation of...Ch. 11.6 - Polar Equation for a Hyperbola A polar equation of...Ch. 11.6 - Polar Equation for a Hyperbola A polar equation of...Ch. 11.6 - Identifying and Graphing a Conic (a) Find the...Ch. 11.6 - Identifying and Graphing a Conic (a) Find the...Ch. 11.6 - Identifying and Graphing a Conic (a) Find the...Ch. 11.6 - Identifying and Graphing a Conic (a) Find the...Ch. 11.6 - Identifying and Graphing a Conic (a) Find the...Ch. 11.6 - Identifying and Graphing a Conic (a) Find the...Ch. 11.6 - Identifying and Graphing a Conic (a) Find the...Ch. 11.6 - Identifying and Graphing a Conic (a) Find the...Ch. 11.6 - Rotating a Conic A polar equation of a conic is...Ch. 11.6 - Rotating a Conic A polar equation of a conic is...Ch. 11.6 - Rotating a Conic A polar equation of a conic is...Ch. 11.6 - Rotating a Conic A polar equation of a conic is...Ch. 11.6 - Families of Conics Graph the conics r = e/(1 e...Ch. 11.6 - Families of Conics (a) Graph the conics...Ch. 11.6 - Orbit of the Earth The polar equation of an...Ch. 11.6 - Perihelion and Aphelion The planets move around...Ch. 11.6 - Orbit of Pluto The distance from Pluto to the sun...Ch. 11.6 - DISCUSS: Distance to a Focus When we found polar...Ch. 11.6 - DISCUSS: Polar Equations of Orbits When a...Ch. 11 - (a) Give the geometric definition of a parabola....Ch. 11 - (a) Give the geometric definition of an ellipse....Ch. 11 - (a) Give the geometric definition of a hyperbola....Ch. 11 - (a) Suppose we are given an equation in x and y....Ch. 11 - (a) How can you tell whether the following...Ch. 11 - (a) Suppose that the x- and y-axes are rotated...Ch. 11 - (a) What is the discriminant of the equation in...Ch. 11 - (a) Write polar equations that represent a conic...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Parabolas An equation of a parabola is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Ellipses An equation of an ellipse is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Path of the Earth The path of the earth around the...Ch. 11 - LORAN A ship is located 40 mi from a straight...Ch. 11 - Families of Ellipses (a) Draw graphs of the...Ch. 11 - Families of Parabolas (a) Draw graphs of the...Ch. 11 - Identifying a Conic An equation of a conic is...Ch. 11 - Identifying a Conic An equation of a conic is...Ch. 11 - Identifying a Conic An equation of a conic is...Ch. 11 - Identifying a Conic An equation of a conic is...Ch. 11 - Identify a Conic from Its Graph Use a graphing...Ch. 11 - Identify a Conic from Its Graph Use a graphing...Ch. 11 - Identify a Conic from Its Graph Use a graphing...Ch. 11 - Identify a Conic from Its Graph Use a graphing...Ch. 11 - Polar Equations of Conics A polar equation of a...Ch. 11 - Polar Equations of Conics A polar equation of a...Ch. 11 - Polar Equations of Conics A polar equation of a...Ch. 11 - Polar Equations of Conics A polar equation of a...Ch. 11 - Find the focus and directrix of the parabola x2 =...Ch. 11 - Find the vertices, foci, and the lengths of the...Ch. 11 - Find the vertices, foci, and asymptotes of the...Ch. 11 - Find an equation for the parabola with vertex (0,...Ch. 11 - Find an equation for the ellipse with foci (3, 0)...Ch. 11 - Find an equation for the hyperbola with foci (0,...Ch. 11 - Find an equation for the conic whose graph is...Ch. 11 - Find an equation for the conic whose graph is...Ch. 11 - Find an equation for the conic whose graph is...Ch. 11 - Determine whether the equation represents an...Ch. 11 - Determine whether the equation represents an...Ch. 11 - Determine whether the equation represents an...Ch. 11 - Find an equation for the ellipse with center (2,...Ch. 11 - Find an equation for the parabola with focus (2,...Ch. 11 - A parabolic reflector for a car headlight forms a...Ch. 11 - (a) Use the discriminant to determine whether the...Ch. 11 - (a) Find the polar equation of the conic that has...Ch. 11 - Conics in Architecture The photographs on page 836...Ch. 11 - Constructing a Hyperbola In this problem we...Ch. 11 - A Parabola in a Rectangle The following method can...Ch. 11 - Hyperbolas from Straight Lines In this problem we...Ch. 11 - Tangent Lines to a Parabola In this problem we...Ch. 11 - A Cut Cylinder In this problem we prove that when...

Find more solutions based on key concepts

Show solutions Using the Point-Slope Form In Exercises 5360, find an equation of the line that passes through the given point ...

Calculus: An Applied Approach (MindTap Course List)

Using the Definition of a Limit In Exercises 7-10, find the limit L. Then use the definition to prove that th...

Calculus: Early Transcendental Functions

Where does the line through (3, 1, 0) and (1, 5, 6) intersect the plane 2x + y z = 2?

Calculus: Early Transcendentals

Find all possible real solutions of each equation in Exercises 3144. (x24x+4)2(x2+6x+5)3=0

Finite Mathematics and Applied Calculus (MindTap Course List)

Prove the statement using the , definition of a limit. limx2(x2+2x7)=1

Single Variable Calculus: Early Transcendentals, Volume I

U se a computer graph of the function to explain why the limit does not exist. 24. lim(x,y)(0,0)xy3x2+y6

Multivariable Calculus

Two sociologists administered questionnaires to samples of undergraduates that measured attitudes toward interp...

Essentials Of Statistics

Which of the following measuring scales are displayed by frequency distribution polygons? a. Either interval or...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the definite integral. 1/21cos(x2)x3dx

Calculus (MindTap Course List)

A population has a mean of =60and a standard deviation of =12. For this population, find the z-score for each o...

Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 90-98, determine whether the statement is true or false. If it is true, explain why it is true. If...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell C...

Single Variable Calculus

Statistical Literacy What is the difference between a parameter and a statistic?

Understanding Basic Statistics

For Problems 1-10, answer true or false. The quotient of two negative integers is a negative integer.

Intermediate Algebra

Demand and Profit To generate a profit from its new oTunes service, OHaganBooks.com needs to know how the deman...

Finite Mathematics

The article Study on the Life Distribution of Microdrills (J. of Engr. Manufacture, 2002: 301-305) reported the...

Probability and Statistics for Engineering and the Sciences

An order reads 0.5 mg of digitalis, and each tablet contains 0.1 mg. How many tablets should be given?

Elementary Technical Mathematics

Determine the range of the following sets of values.
13. 4 9 3 5 4 7 1 9 9 4 7 1 8 1 4 6 7 4 6 9 9 2

Contemporary Mathematics for Business & Consumers

In concave hexagon HJKLMN, mH=72. Exterior angles at J and L arc formed by extensions of HJ and ML. Bisector JP...

Elementary Geometry For College Students, 7e

Find a counterexample to show that the following conjecture is false. Conjecture: For all numbers x,(x+4)2=x2+1...

Mathematical Excursions (MindTap Course List)

In Problems 17 and 18, approximate the real solutions to each quadratic equation to two decimal places.

Mathematical Applications for the Management, Life, and Social Sciences

Reflective Property Use a sketch to illustrate the reflective property of an ellipse.

Calculus of a Single Variable

Find the values of p for which the series is convergent. 31. n=1n(1+n2)p

Single Variable Calculus: Early Transcendentals

Verifying a Formula In Exercises 4752, verify the integration formula. una+budu=2(2n+1)(una+bunaun1a+budu)

Calculus: Early Transcendental Functions (MindTap Course List)

For the matrices in Exercise 12, evaluate (A+B)2 and A2+2AB+B2 and compare the results.

Elements Of Modern Algebra

Convert each of the following to degrees and minutes. 43.85

Trigonometry (MindTap Course List)

limx0cscx= a) 0 b) c) d) does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

is a(n):
ellipsoid
elliptic cone
elliptic paraboloid
elliptic cylinder

Study Guide for Stewart's Multivariable Calculus, 8th

Use the Distance Formula to show that the circle with center 0, 0 and radius length r has the equation x2+y2=r2...

Elementary Geometry for College Students

In Exercises 21-26, state the negation of the proposition. New orders for manufactured goods fell last month.

Finite Mathematics for the Managerial, Life, and Social Sciences

ProofProve that aN=vav.

Multivariable Calculus

Evaluating a Definite Integral Using a Geometric Formula In Exercises 23-32, sketch the region whose area is gi...

Calculus (MindTap Course List)

A sample of 16 items provides a sample standard deviation of 9.5. Test the following hypotheses using = .05. W...

Statistics for Business & Economics, Revised (MindTap Course List)

The following 20 observations are for two quantitative variables, x and y. a. Develop a scatter diagram for the...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A random sample of n = 12 four-year-old red pine trees was selected, and the diameter (in inches) of each trees...

Introduction To Statistics And Data Analysis

Use the method of Example 9 to do each calculation. Write all answers in scientific notation. (0.000000045)(0.0...

College Algebra (MindTap Course List)

Express the following decimal numbers as binary numbers. 100

Mathematics For Machine Technology

For a two-factor research study with two levels for factor A and four levels for factor B. how many participant...

Research Methods for the Behavioral Sciences (MindTap Course List)

In an experiment examining human memory, two groups of participants are used. One group is allowed 5 minutes to...

Research Methods for the Behavioral Sciences (MindTap Course List)

In Exercises 3338, use Exercise 32 to find the odds that a card dealt from a full deck no jokers is as stated. ...

Mathematics: A Practical Odyssey