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Chapter 10: Q. 24 (page 667)

In Problems 19鈥�28, find an equation for the hyperbola described. Graph the equation by hand. Focus at (0,6); vertices at (0,-2) and(0,2).

Short Answer

Expert verified

Equation of the hyperbola is:y24-x232=1

Graph of the hyperbola is:

Step by step solution

01

Step 1. Given information 

Hyperbola with Focus at (0,6); vertices at (0,-2)and (0,2).

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 focus at (0,6); vertices at (0,-2)and (0,2).

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

We get, a=2,c=6

b2=c2-a2鈬�b2=62-22鈬�b2=36-4鈬�b2=32鈬�b=卤42

Substituting aand bin the equation,

y24-x232=1

04

Step 4. Graphing the hyperbola

To determine the opening of hyperbola, substitute y=卤6in the equation and find x.

卤624-x232=1鈬�x232=364-1鈬�x2=32脳324鈬�x=卤16

The graph of the hyperbola is:

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