   Chapter 10.5, Problem 43E

Chapter
Section
Textbook Problem

# Find an equation for the conic that satisfies the given conditions.43. Hyperbola, vertices (±3, 0), foci (±5, 0)

To determine

To Find: The equation for the conic using the vertices (±3,0) and foci (±5,0) of the Hyperbola.

Explanation

Given:

The vertices and foci of the hyperbola are (±3,0) and foci (±5,0) .

Calculation:

The foci and vertices are located in x axis.

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

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

vertices=((h±a),k)

Substitute (0,0) for (h,k) and (±3,0) for vertices.

(±3,0)=((h±a),k)(0±a)=±3a=±3

The value of a is +3 .

Compute the value of c using the equation below.

foci=(h,(k±c))

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

(±5,0)=((0±c),0)±5=(0±c)c=±5

Therefore, the value of c is ±5

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