   Chapter 10.5, Problem 37E

Chapter
Section
Textbook Problem

# Find an equation for the conic that satisfies the given conditions.37. Ellipse, foci (±2, 0), vertices (±5, 0)

To determine

To Find: The equation for the conic using the foci (±2,0) and the vertices (±5,0) of the ellipse.

Explanation

Given:

The foci are (±2,0) and the vertices are (±5,0) of the ellipse.

Calculation:

Since, the y coordinate of the foci and vertices is zero. The value of k is 0 .

Center of the ellipse (h,k) is (0,0) .

Compute the value of a using the vertices equation.

vertices=((h±a),k)

Substitute the value of (±5,0) for vertices and (0,0) for (h,k) .

(±5,0)=((h±a),k)k=0(h±a)=±5(0±a)=±5a=±5

Therefore, the value of a is ±5 .

foci=((h±c),k)

Substitute the value (±2,0) for foci and (0,0) for (h,k) .

(±2,0)=((h±c),k)k=0(h±c)=±2(0±c)=±2c=±2

Compute the value of b

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