Chapter 10, Problem 23RE

### 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: ( ± 7 , − 1 ) Vertex: ( ± 9 , − 1 )

To determine

To calculate: The standard form of the equation of the hyperbola with Vertices (±7,1) and Foci (±9,1).

Explanation

Given:

Vertices: (Â±7,âˆ’1)

Foci: (Â±9,âˆ’1)

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±7,âˆ’1) and the foci as, (Â±9,âˆ’1).

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

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

Compare it with the standard form,

k=âˆ’1

Here,

2h=0h=0

And,

h+a=7a=7âˆ’0=7

Also,

h+c=9c=9âˆ’0=9

For a hyperbola,

c2=a2+b2

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 29-34, rationalize the denominator of each expression. 30. 1x+5

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 63-73, factor each expression completely. 67.

Mathematical Applications for the Management, Life, and Social Sciences

#### Using for |x| < 1,

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th