Chapter 10, Problem 22RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding the Standard Equation of a Hyperbola In Exercises 21-24, find the standard form of the equation of the hyperbola with the given characteristics.Vertices: ( ± 2 , 0 ) Asymptotes: y = ± 32 x

To determine

To calculate: The standard form of the equation of the hyperbola whose vertices are given as, (±2,0) and asymptotes as, y=±32x.

Explanation

Given:

Vertices: (Â±2,0)

Asymptotes: y=Â±32x

Formula used:

The standard equation of a hyperbola with center (h,k), focus (hÂ±c,k) and vertex (hÂ±a,k) is,

(xâˆ’h)2a2âˆ’(yâˆ’k)2b2=1

Calculation:

The vertices of a hyperbola are given as, (Â±2,0) and the asymptotes as, y=Â±32x.

On observing the vertices, it can be seen that the hyperbola has a horizontal transverse axis.

For a hyperbola with a horizontal transverse axis, the center is (h,k), focus (hÂ±c,k) and vertex (hÂ±a,k).

Compare with the standard form,

k=0

Here,

2h=0h=0

And,

h+a=2a=2âˆ’0=2

Also, the general form of asymptotes is y=kÂ±ba(xâˆ’h)

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