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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

21-28 ■ Graphing Shifted Hyperbolas An equation of hyperbola is given. (a) Find the centre, vertices, foci, and asymptotes of the hyperbola. (b) Sketch a graph showing the hyperbola and its asymptotes.

36 x 2 + 72 x 4 y 2 + 32 y + 116 = 0

To determine

(a).

To find:

The center, vertices, foci, and asymptotes of the given hyperbola.

Explanation

Given:

An equation of hyperbola

36x2+72x4y2+32y+116=0

Approach:

Completing the square of given equation, we get the equation of shifted hyperbola, then comparing the equation of given hyperbola with equation of shifted hyperbola,

(yk)2a2(xh)2b2=1

Calculation:

Rearranging equation of hyperbola, we get

36x2+72x4y2+32y+116=036(x2+2x)4(y28y)+116=036(x2+2x+1)364(y28y+16)+64+116=036(x+1)24(y4)2=144

(y4)236(x+1)24=1

The shifted hyperbola has center, C(-1, 4) and It is an up-down hyperbola

To determine

(b).

To draw:

A graph showing the hyperbola and its asymptotes.

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