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Chapter 10: Q. 44 (page 668)

In Problems 41鈥� 48, find an equation for the hyperbola described. Graph the equation by hand. Center at (1,4); focus at (-2,4); vertex at(0,4).

Short Answer

Expert verified

Equation of the hyperbola is:(x-1)2-(y-4)28=1

Graph of the hyperbola is:

Step by step solution

01

Step 1. Given information 

Hyperbola with center at (1,4); focus at (-2,4); vertex at (0,4).

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)=(1,4)Focus:(-c+h,k)=(-2,4)鈬�c=3Vertex:(-a+h,k)=(0,4)鈬�a=1b2=c2-a2鈬�b2=32-12鈬�b2=9-1鈬�b2=8鈬�b=卤22

Substituting for h,k,aandbin the standard equation,

(x-1)21-(y-4)28=1鈬�(x-1)2-(y-4)28=1

03

Step 3. Graph of the hyperbola 

Equations of asymptotes:

(y-k)=卤ba(x-h)鈬�(y-4)=卤22(x-1)

Graph of the hyperbola is:

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