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Chapter 10: Q. 41 (page 668)

In Problems 41鈥� 48, find an equation for the hyperbola described. Graph the equation by hand. Center at (4,-1); focus at (7,-1); vertex at(6,-1).

Short Answer

Expert verified

Equation of the hyperbola is:(x-4)24-(y+1)25=1

Graph of the hyperbola is:

Step by step solution

01

Step 1. Given information 

Hyperbola with center at (4,-1); focus at (7,-1); vertex at (6,-1).

02

Step 2. Finding the equation of the hyperbola  

Comparing the given hyperbola with the standard form,

(x-h)2a2-(y-k)2b2=1,b2=c2-a2Center:(h,k)=(4,-1)Focus:(c+h,k)=(7,-1)鈬�c=3Vertex:(a+h,k)=(6,-1)鈬�a=2b2=c2-a2鈬�b2=32-22鈬�b2=9-4鈬�b2=5鈬�b=卤5

Substituting forh,k,aandbin the standard equation,

(x-4)24-(y+1)25=1

03

Step 3. Graph of the hyperbola

Equations of asymptotes:

(y-k)=卤ba(x-h)鈬�(y+1)=卤52(x-4)

Graph of the hyperbola is:

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