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Chapter 10: Q. 25 (page 667)

In Problems 19鈥�28, find an equation for the hyperbola described. Graph the equation by hand. Vertices at (0,-6)and (0,6); asymptote the liney=2x.

Short Answer

Expert verified

Equation of the hyperbola:y236-x29=1

Graph of the hyperbola:

Step by step solution

01

Step 1. Given information 

Hyperbola with vertices at (0,-6)and (0,6); asymptote the liney=2x.

02

Step 2. Required to find 

Find the equation of the hyperbola. Graph the equation.

03

Step 3. Finding the equation of the hyperbola 

Given, hyperbola with vertices at (0,-6)and (0,6); asymptote the line y=2x.

Comparing with standard form of hyperbola, y2a2-x2b2=1,b2=c2-a2;vertices=(0,卤a);asymptotes,y=卤abx

We get,

role="math" localid="1646999569672" a=6,ab=2鈬�b=a2鈬�b=62鈬�b=3

Substituting aand bin the equation,

y236-x29=1

04

Step 4. Graphing the hyperbola 

Graph of the hyperbola:

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