   Chapter 10.5, Problem 39E

Chapter
Section
Textbook Problem

Find an equation for the conic that satisfies the given conditions.39. Ellipse, foci (0, 2), (0, 6), vertices (0, 0), (0, 8)

To determine

To Find: The equation for the conic using the foci (0,2) , (0,6) and the vertices (0,0) , (0,8) of the ellipse.

Explanation

Given:

The foci points are (0,2) , (0,6) and the vertices are (0,0) , (0,8) of the ellipse.

Calculation:

The x coordinate of the foci and vertices is zero.

The value of h is 0 and the foci and vertices are located in y axis.

Compute the center of the ellipse and the value of a using the vertices equation.

vertices=(h,(k±a))

The points of vertices are (0,0) and (0,8) .

Assume that the value of a is 4 and the value of k is 4 .

(0,0),(0,8)=(h,(k±a))h=0(k+a)=(4+4)(k+a)=8(ka)=(44)(ka)=0

Therefore, center of the ellipse (h,k) is (0,4) and the value of a is 4 .

Compute the value of c from the below equation.

foci=(h,(k±c))

Substitute the value (0,2),(0,6) for foci and (0,4) for (h,k)

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