   Chapter 12.CR, Problem 58E ### 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

# 55-64 ■ Find the Equation of the Conic Find an equation for the conic section with the given properties.58. The hyperbola with vertices V ( 0 , ± 2 ) and asymptotes y = ± 1 2 x .

To determine

To find:

An equation for the hyperbola with vertices V(0,±2), and asymptotes y=±12x.

Explanation

Given:

The vertices and asymptotes of a hyperbola are V(0,±2) and y=±12x.

Approach:

Standard equation of the hyperbola is (yk)2a2(xh)2b2=1, having center (h,k) and asymptotes are yk=±ab(xh).

Calculation:

The vertices of a hyperbola are V(0,±2), vertices are lying on y-axis and center is the midpoint of the vertices, so the center is (h,k)=(0,0). The axis of hyperbola is along the y-axis, so it is a up and down hypebola. For a up and down hyperbola having center at origin, the asymptotes are as follows,

y=±abx

Compare the given equation of asymptotes with above equation, so ab=12. The distance between vertex and center is the value of a, so a=2, and b=4

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