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Chapter 10: Q. 20 (page 683)

In Problems 13鈥�24, analyze each equation and graph it

r=82+4cos胃

Short Answer

Expert verified

The given represents a hyperbola.

Step by step solution

01

Step 1. Given Information 

We are given an equation

r=82+4cos胃

We need to find the graph of the equation.

02

Step 2. Analyze the equation 

Compare the given equation with r=ep1+ecos胃

The given equation becomes,

r=82+4cos胃路1212r=41+2cos胃

Therefore,

e=2ep=4鈬�(2)p=4鈬�p=42=2

Since e>1, therefore it is a hyperbola.

03

Step 3. Plotting points 

Now, we will calculate the points from the given equation,

胃=0:r=82+4cos(0)=82+4=86=4343,0胃=蟺2:r=82+4cos蟺2=82+0=82=44,蟺2胃=蟺:r=82+4cos(蟺)=82-4=8-2=-4(-4,蟺)胃=3蟺2:r=82+4cos3蟺2=82+0=82=4

04

Step 4. Required graph

Plotting the points, we get the graph as,

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