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Chapter 10: Q. 42 (page 668)

In Problems 41鈥� 48, find an equation for the hyperbola described. Graph the equation by hand. Center at (-3,1); focus at (-3,6); vertex at(-3,4).

Short Answer

Expert verified

Equation of the hyperbola is:(y-1)29-(x+3)216=1

Graph of the hyperbola is:

Step by step solution

01

Step 1. Given information 

Hyperbola with center at (-3,1); focus at (-3,6); vertex at(-3,4).

02

Step 2. Finding the equation of the hyperbola  

Comparing the given hyperbola with the standard form,

(y-h)2a2-(x-k)2b2=1,b2=c2-a2Center:(h,k)=(-3,1)Focus:(h,c+k)=(-3,6)鈬�c=5Vertex:(h,a+k)=(-3,4)鈬�a=3b2=c2-a2鈬�b2=52-32鈬�b2=25-9鈬�b2=16鈬�b=卤4

Substituting for h,k,aandbin the standard equation,

role="math" localid="1647154554917" (y-1)29-(x+3)216=1

03

Step 3. Graph of the hyperbola 

Equations of asymptotes:

(y-k)=卤ab(x-h)鈬�(y-1)=卤34(x+3)

Graph of the hyperbola is:

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