   Chapter 12.6, Problem 46E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# DISCUSS:Distance to a Focus When we found the polar equations for the conics, we placed one focus at the pole. It’s easy to find the distance from that focus to any point on the conic. Explain how the polar equation gives us this distance.

To determine

To discuss:

How polar equation gives us the distance between any point on the conic and focus of the conic.

Explanation

In the derivation of the polar equation of conic, we placed one focus at the origin and other focus at the pole. A distance of any point from the focus at origin is simply r.

Denote the point on the conic by P and the focus at origin by F1 and the focus at the pole by F2.

For an ellipse we know:

PF1+PF2=2a

where 2a is the length of the major axis, PF1 denotes the distance of P from F1, PF2 denotes the distance of P from F2.

Using: PF1=r, we get:

PF2=2ar

For a hyperbola we know:

|PF1PF2|=2a

where 2a is the length of the major axis, PF1 denotes the distance of P from F1 (origin), PF2 denotes the distance of P from F2.

Using: PF1=r, we can obtain PF2

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