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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Find an equation for the conic that satisfies the given conditions.

40. Ellipse, foci (0, −1), (8, −1), vertex (9,−1)

To determine

To Find: The equation for the conic using the foci (0,1) , (8,1) and the vertex (9,1) of the ellipse.

Explanation

Given:

The foci (0,1) , (8,1) and the vertex (9,1) of the ellipse.

Calculation:

Since, the y coordinate of the foci and vertex is same and equal to 1 . Then, the value of k is 1 and the foci and vertices are located in x axis.

Compute the value of c and the center from the below equation.

foci=((h±c),k)

The foci points are (0,1) , and (8,1) .

Assume that the value of c is 4 and the value of h is 4 .

(0,1)=((h±c),k)k=1(hc)=0(44)=0

(8,1)=((h±c),k)k=1(h+c)=8(4+4)=8c=8

Hence, the value of c is 4 and the center of ellipse (h,k) is (4,1) .

Compute the value of a using the vertices equation.

vertices=((h±a),k)

Substitute the value of (9,1) for vertex, (4,1) for (h,k) and 4 for c

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