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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

Graphing Hyperbolas An equation of a hyperbola is given. (a) Find the vertices, foci, and asymptotes of the hyperbola. (b) Determine the length of the transverse axis. (c) Sketch a graph of the hyperbola.

y 2 x 2 25 = 1

To determine

(a)

To find:

The vertex, foci, and asymptotes of the hyperbola.

Explanation

Given:

The equation of the hyperbola:

y2x225=1

Approach:

If the hyperbola equation is y2a2x2b2=1, then the vertices, foci and asymptotes can be calculated as follows:

Vertex: (0,a) and (0,a)

Foci: (0,c) and (0,c), where c=a2+b2

Asymptotes: y=abx and y=abx

Calculation:

Compare the following two equation:

y2a2x2b2=1

y2x225=1

The obtained value of a is 1 and b is 5, so vertices are (0,1) and (0,1)

To determine

(b)

To find:

The length of transverse axis,

To determine

(c)

To plot:

The graph of the hyperbola y2x225=1.

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