   Chapter 10, Problem 23RE

Chapter
Section
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: (±7,1)

Foci: (±9,1)

Formula used:

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

(xh)2a2(yk)2b2=1

Calculation:

The vertices of a hyperbola are given as, (±7,1) and the foci as, (±9,1).

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 (h±c,k) and vertex (h±a,k).

Compare it with the standard form,

k=1

Here,

2h=0h=0

And,

h+a=7a=70=7

Also,

h+c=9c=90=9

For a hyperbola,

c2=a2+b2

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