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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.

( x + 1 ) 2 9 ( y + 1 ) 2 4 = 1

To determine

(a).

To find:

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

Explanation

Given:

An equation of hyperbola

(x+1)29(y+1)24=1

Approach:

Compare the equation of given hyperbola with equation of shifted hyperbola,

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

Calculation:

The shifted hyperbola has center, C(-1,-1) and has a horizontal transverse axis.

Its graph will have similar shape as the unshifted hyperbola

x29y24=1 (Center origin)

Since a2=9 and b2=4, we get a=3, b=2, and c=a2+b2=9+4=13. Thus the foci will lie 13 units to the right and to the left of the center, and the vertices will lie 3 units to either side of the centre.

Foci F(2.606,1) and F(4

To determine

(b).

To draw:

A graph showing the hyperbola and its asymptotes.

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