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7th Edition

James Stewart + 2 others

Publisher: Brooks Cole

ISBN: 9781305071759

Chapter 11.4, Problem 67E

Textbook Problem

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**Orbit of a Satellite** A satellite is in an elliptical orbit around the earth with the center of the earth at one focus, as shown in the figure. The height of the satellite above the earth varies between 140 mi and 440 mi. Assume that the earth is a sphere with radius 3960 mi. Find an equation for the path of the satellite with the origin at the center of the earth.

To determine

**To find:** The equation for the path of the satellite with the origin at the center of the earth which rounds the earth in an elliptical orbit with its height varies from 140m and 440m from the surface of the earth.

**Definition used:**

**Definition 1:**

“The equation of the shifted ellipse with center
*x*-axis) axis has the major axis is

**Calculation:**

The path of the satellite is elliptic around the earth and one of its focus is the center of the earth.

Since, the center of the earth is the focus.

Let

The horizontal line through *F* has the *x*-axis and the perpendicular to the *x*- axis at *F* has the *y*-axis.

Therefore,

The given radius of the earth is 3960mi.

The least distance of the satellite from the surface of the earth is 140mi.

The least distance of the satellite from its center of the earth is

That is the coordinate of *A* is

Also, the farthest distance of the satellite from the surface of the earth is 440mi.

The farthest distance of the satellite from its center of the earth is

Therefore, the coordinate of

Precalculus: Mathematics for Calculus (Standalone Book)

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(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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