Step by step solution to "How do you find the points of intersection..."

Kai Ashley

Answered question

2022-02-12

How do you find the points of intersection of the curves with polar equations

r = 6 \cos θ and r = 2 + 2 \cos θ

maskorfclp

Beginner2022-02-13Added 12 answers

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

6 \cos (θ) = 2 + 2 \cos (θ)

And solving for

θ

you get:

6 \cos (θ) - 2 \cos (θ) = 2

4 \cos (θ) = 2

\cos (θ) = \frac{1}{2}

which is valid:
for

θ = \frac{π}{3} and θ = 5 \frac{π}{3}

Substituting back you get:

r = 6 \cos (θ) = 6 \cdot \frac{1}{2} = 3

r = 2 + 2 \cos (θ) = 2 + 2 \cdot \frac{1}{2} = 3

again.
Giving 2 points of intersection:

(3, \frac{π}{3})

(3, \frac{5}{3} π)

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