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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

55–64Finding the Equation of a Conic Find an equation for the conic section with the given properties.

The ellipse with vertices V 1 ( 7 , 12 ) and V 2 ( 7 , 8 ) and passing through the point P ( 1 , 8 ) .

To determine

To find:

The equation for the ellipse with vertices V1(7,12) and V2(7,8) and passing through the point P(1,8).

Explanation

Approach:

The midpoint of vertices is the center of the ellipse.

Length of major axis is the distance between the center and a vertex.

The equation of ellipse with vertical major axis is given by:

(yk)2a2+(xh)2b2=1.

Calculation:

By midpoint formula, center is (7+72,1282)=(7,2).

Length of major axis is 10, so a=10.

The equation of ellipse is

(yk)2a2+(xh)2b2=1(y2)2100+(x7)2b2=1

The ellipse passes through the point P(1,8)

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Chapter 12 Solutions

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