How do you find the points of intersection of the curves with polar equations r=6costheta and r=2+2costheta?

1 Answer
Gió
Feb 4, 2015

I would substitute the first equation into the second for r, giving:

6cos(theta)=2+2cos(theta)

And solving for theta you get:

6cos(theta)-2cos(theta)=2

4cos(theta)=2

cos(theta)=1/2 which is valid:

for theta=pi/3 and theta=5pi/3

Substituting back you get:
r=6cos(theta)=6*1/2=3
or
r=2+2cos(theta)=2+2*1/2=3 again.
Giving 2 points of intersection:
(3,pi/3)
(3,5/3pi)
Graphically:
enter image source here

hope it helps

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