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Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759

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BuyFindarrow_forward

Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759
Chapter 11, Problem 9RE
Textbook Problem
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Graphing Parabolas An equation of a parabola is given. (a) Find the vertex, focus, and directrix of the parabola. (b) Sketch a graph of the parabola and its directrix.

9. 1 2 ( y 3 ) 2 + x = 0

(a)

To determine

To find: The vertex, focus and directrix of the parabola 12(y3)2+x=0 .

Explanation of Solution

Definition used:

“The equation of shifted parabola with vertex V(h,k) is (yk)2=4p(xh) ”.

“The equation of the parabola with vertex V(0,0) , focus F(p,0) and directrix x=p is y2=4px ”.

“If h and k are any two positive real numbers and a graph of any equation is in terms of x and y then.

(i) Replacing x by xh , shift the graph right to h units.

(ii) Replacing x by x+h , shift the graph left to h units.

(iii) Replacing y by yk , shift the graph upward to k units.

(iv) Replacing y by y+k , shift the graph downward to k units.”

The given equation of conic is 12(y3)2+x=0 .

Given the equation of conic 12(y3)2+x=0 can be rewritten as,

12(y3)2+x=012(y3)2=x(y3)2=2x

Therefore, the given conic is (y3)2=2x .

Use the definition “The equation of shifted parabola with vertex V(h,k) is (yk)2=4p(xh) ” in the equation of parabola (y3)2=2x .

Here, h=0 and k=3 .

Therefore, by above definition the vertex of the parabola (y3)2=2x is V(0,3,) .

The equation (y3)2=2x is the shifted parabolic equation of y2=2x

(b)

To determine

To sketch: The graph and directrix of the parabola (y3)2=2x .

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Chapter 11 Solutions

Precalculus: Mathematics for Calculus (Standalone Book)
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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 - 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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...

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