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Another ellipse construction Start with two circles

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 53RE Chapter 10

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 53RE

Another ellipse construction Start with two circles centered at the origin with radii 0<a<b (see figure). Assume the line ℓ though the origin intersects the smaller circle al Q and the larger circle at R. Let P(x, y) have the y-coordinate of Q and the x-coordinate of R. Show that the set of points P(x, y) generated in this way for all lines ℓ through the origin is an ellipse.

Step-by-Step Solution:

Solution 53RE

Step 1:

In this problem we need to show that the set of points P(x, y) generated in this way for all lines  through the origin is an ellipse.

Given :

Two circles with centers at origin and radii a, b where a<b.

The line l through origin intersects the smaller circle at Q and the larger circle at R.

Let P(x,y) is a point such that it has y-coordinate of Q and x-coordinate of R.

We have to show that the set of points P(x, y) generated in this way for all lines  through the origin is an ellipse.

Step 2 of 3

Chapter 10, Problem 53RE is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Another ellipse construction Start with two circles