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Chapter 9: Q. 70 (page 584)

In Problems 67鈥�70, the polar equation for each graph is either r=a+bcos胃or r=a+bsin胃,a>0. Select the correct equation and find the values of aand b.

Short Answer

Expert verified

The correct equation for the graph is r=1+4sin胃

And the value of a is 1and bis4

Step by step solution

01

Step 1. Given

The graph:

The polar equations:

r=a+bcos胃r=a+bsin胃

02

Step 2. Test for r=a+b cos θ

Substitute the point (1,0)from the graph in the equation,

r=a+bcos胃1=a+bcos(0)1=a+b

Substitute the point (5,蟺2)from the graph in the equation,

5=a+bcos(蟺2)5=a

03

Step 3. Find b 

Substitute a=5in the equation,

5+b=1b=-4

Since b>0, it is not a correct equation, so test the other equation.

04

Step 4. Test the equation r=a+b sin θ

Substitute (1,0)in the equation,

1=a+bsin(0)a=1

Substitute (5,蟺2)in the equation,

5=1+bsin(蟺2)5-1=bb=4

05

Step 5. Find the equation

Substitute a=1;b=4in the suitable equation,

r=1+4sin胃

The polar equation of the given graph is r=1+4sin胃

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Most popular questions from this chapter

find the unit vector in the same direction asvv=3i-4j

Find ||v||. If v=6i+2j

True or False The tests for symmetry in polar coordinates are necessary but not sufficient.

Identify and graph each polar equation. Verify your graph using a graphing utility.
r=2+4cos胃

Identify and graph each polar equation. Verify your graph using a graphing utility.

r=2胃
See all solutions

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