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7th Edition

James Stewart + 2 others

Publisher: Brooks Cole

ISBN: 9781305071759

Chapter 11.6, Problem 45E

Textbook Problem

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**Orbit of Pluto** The distance from Pluto to the sun is 4**.**43 × 10^{9} km at perihelion and 7.37 × 10^{9} km at aphelion. Use Exercise 44 to find the eccentricity of Pluto’s orbit.

To determine

**To find:** The eccentricity of Pluto’s orbit with the distance from the sun is

**Definition used:**

**Definition 1:**

“A planet around the sun one in elliptical orbit with sun at one focus.

The perihelion distance of planet to the sun is

The aphelion distance of the planet to the sun is

**Calculation:**

The perihelion and aphelion distances to the sun is

That is, by definition stated above,

Thus, the perihelion distance

Use above equation and find the value of

Precalculus: Mathematics for Calculus (Standalone Book)

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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 - 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