   Chapter 10.1, Problem 43E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

By definition, an ellipse is the locus of points whose sum of distances from two fixed points F 1 and F 2 (called foci) is constant. In the grid provided, find points whose sum of distances from points F 1 3, 0 and F 2 - 3, 0 is 10. That is, locate some points for which P F 1 + P F 2 = 10 ; point P 5, 0 is one such point. Then sketch the ellipse.

To determine

To sketch:

The ellipse using the given data.

Explanation

The general equation of the ellipse is shown below.

x2a2+y2b2=1

Vertices ±a, 0.

Endpoints of minor axis 0, ±b

Foci ±c, 0

Here c2=a2-b2

The foci of the ellipse is F13, 0 and F2-3, 0.

Since, foci ±c, 0

Hence, c=3

In the problem, it is given that one point is 5, 0.

Vertices ±a, 0

The other point is -5, 0.

Since PF1+PF2=10

2a=10

Dividing by 2,

2a2=102

From this,

a=5

Using the values of a and c, we have to find b

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