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Chapter 10: Q. 20 (page 667)

In Problems 19鈥�28, find an equation for the hyperbola described. Graph the equation by hand. Center at (0,0); focus at (0,5); vertex at (0,3).

Short Answer

Expert verified

Equation of the hyperbola is:y29-x216=1

Graph of the hyperbola is:

Step by step solution

01

Step 1. Given information  

Hyperbola with Center at (0,0); focus at (0,5); vertex at(0,3).

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 Center at (0,0); focus at (0,5); vertex at (0,3).

Comparing with standard form of hyperbola, localid="1646825525683" y2a2-x2b2=1,b2=c2-a2;foci=(0,卤c);vertices=(0,卤a)

We get, localid="1646825530337" a=3,c=5

b2=c2-a2鈬�b2=52-32鈬�b2=25-9鈬�b2=16鈬�b=卤4

Substituting aand role="math" localid="1646825552217" bin the equation,

localid="1646825556348" y29-x216=1

04

Step 4. Graphing the hyperbola

To determine the opening of hyperbola, substitute x=卤4in the equation and find y.

y29-卤4216=1鈬�y29=1+1鈬�y2=18鈬�y=卤32

The graph of the hyperbola is:

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