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Chapter 10: Q. 19 (page 683)

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

r=82-sin胃

Short Answer

Expert verified

The equation represents an ellipse.

Step by step solution

01

Step 1. Given Information 

We are given an equation

r=82-sin胃

We need to find the graph of the equation,

02

Step 2. Analyze the equation 

Compare the given equation with r=ep1-esin胃

The given equation becomes,

r=82-sin胃路1212r=41-12sin胃

Here,

e=12ep=4鈬�12p=4鈬�p=21(4)=8

Since,e<1, therefore, it is an ellipse.

03

Step 3. Plotting points 

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

胃=0:r=82-sin(0)=82-0=82=4胃=蟺2:r=82-sin蟺2=82-1=81=8胃=蟺:r=82-sin(蟺)=82-0=82=4胃=3蟺2:r=82-sin3蟺2=82+1=8383,3蟺2

04

Step 4. Required graph

Plotting the points, we get the graph as,

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