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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 the vertices, foci, and asymptotes of the hyperbola and sketch its graph.

20. x 2 36 y 2 64 = 1

To determine

To find: The vertices, foci and asymptotes of the hyperbola for the equation x236y264=1 and sketch the graph.

Explanation

Given:

The hyperbola equation is as follows.

x236y264=1 (1)

Formula used:

Then, compare the equation (1) with the standard equation of hyperbola,

x2a2y2b2=1 (2)

Calculation:

Compute the center of the hyperbola using the equation.

(xh)2a2+(yk)2b2=1(y0)236+(x0)264=1

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

Substitute the value 36 for a2 and 64 for b2 in equation (2),

a2=36a=36a=6

b2=64b=64b=8

Compute the vertices:

The vertices are said to be ((h±a),k).

Substitute the value 6 for a.

Then, the vertices of the hyperbola are (±6,0)_.

Compute the value of c using the equation below.

c2=a2+b2

Substitute the value 6 for a and 9 for b

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Chapter 10 Solutions

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