   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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