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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
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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Chapter 10 Solutions

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P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

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