   Chapter 10.5, Problem 44E

Chapter
Section
Textbook Problem

# Find an equation for the conic that satisfies the given conditions.44. Hyperbola, vertices (0, ±2), foci (0, ±5)

To determine

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

Explanation

Given:

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

Calculation:

The foci and vertices are located in y axis.

Therefore, the center of the hyperbola (h,k) is (0,0) .

Find the value of a and the equation of foci as below.

vertices=(h,(k±a))

Substitute (0,0) for (h,k) and (0,±2) for vertices.

(0,±2)=(h,(k±a))h=0(0±a)=±2a=±2

Therefore, the value of a is ±2 .

Compute the value of c using the equation below.

foci=((h±c),k)

Substitute (0,0) for (h,k) and (0,±5) for foci.

(0,±5)=((h±c),k)k=0(0±c)=±5c=±5

Therefore, the value of c is ±5

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