How do you find the rectangular equation for r=2+2costhetar=2+2cosθ?

1 Answer
Douglas K.
Oct 17, 2016

x^2 + y^2 - 2x - 2sqrt(x^2 + y^2) = 0x2+y2−2x−2√x2+y2=0

Explanation:

Multiply both sides by r:

r^2 = 2r + 2rcos(theta)r2=2r+2rcos(θ)

Substitute sqrt(x^2 + y^2)√x2+y2 for rr, x^2 + y^2x2+y2 for r^2r2 and xx for rcos(theta)rcos(θ)

x^2 + y^2 = 2sqrt(x^2 + y^2) + 2xx2+y2=2√x2+y2+2x

Move everything to the left:

x^2 + y^2 - 2x - 2sqrt(x^2 + y^2) = 0x2+y2−2x−2√x2+y2=0

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