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Chapter 10: Q. 22 (page 683)

In Problems 13鈥�24, analyze each equation and graph it. r(2-cos胃)=2

Short Answer

Expert verified

The equation represents an ellipse.

Step by step solution

01

Step 1. Given Information 

We are given an equation

r(2-cos胃)=2

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=22-cos胃r=22-cos胃路1212r=11-12cos胃OnComparing,e=12andep=1鈬�12p=1鈬�p=21(1)=2

Sincee<1, therefore, it is an ellipse.

03

Step 3. Plotting points 

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

胃=0:r=22-cos(0)=22-1=21=2胃=蟺2:r=22-cos蟺2=22-0=22=1胃=蟺:r=22-cos(蟺)=22+1=2323,蟺胃=3蟺2:r=22-cos蟺2=22-0=22=1

04

Step 4. Required graph 

Plotting the points, we get the graph as,

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Most popular questions from this chapter

True or False

To eliminate the xy-term from the equation x2-2xy+y2-2x+3y+5=0, rotate the axes through an angle 胃, where cot胃=B2-4AC.

2. To complete the square of x2-4x,add _______.

Use the Square Root Method to find the real solutions of (x+4)2=9.

The point that is symmetric with respect to the y-axis to the point (-2,5)is _____.

Transform the equation r=6cos(胃)from polar coordinate to rectangular coordinate.
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