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Chapter 10: Q. 16 (page 683)

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

r=105+4cos胃

Short Answer

Expert verified

The given equation represents a ellipse.

The graph of the equation is

Step by step solution

01

Step 1. Given Information

We are given an equation

r=105+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=105+4cos胃路1515r=21+45cos胃

Therefore,

e=45<145p=2p=52

Since,e<1therefore the equation represents a ellipse.

03

Step 3. Plotting points

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

At胃=0:r=105+4cos(0)=105+4=109At胃=蟺2:r=105+4cos蟺2=105+0=105=22,蟺2At胃=蟺:r=105+4cos(蟺)=105-4=101=10At胃=3蟺2:r=105+4cos3蟺2=105+0=105=22,3蟺2

04

Step 4. Required graph

Plotting the points, we get the graph as,

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