   Chapter 12.3, Problem 11E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### 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 36 − x 2 4 = 1

To determine

(a)

To find:

The vertex, foci, and asymptotes on the hyperbola,

Explanation

Given:

The equation of the hyperbola is:

y236x24=1

Approach:

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

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 equations:

y2a2x2b2=1

y236x24=1

The obtained value of a is 6 and b is 2, so vertices are (0,6), (0,6).

The value of c is given by,

To determine

(b)

To find:

The length of transverse axis.

To determine

(c)

To plot:

The hyperbola equation y236x24=1.

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