Question

Write the polar equation in rectangular form. r = 12 sin theta

Write the rectangular equation (x + 7)^2 + y^2 = 49 in polar form

Answer 1

r = 12 sinθ
r^2 = 12r sinθ
x^2+y^2 = 12x
x^2 - 12x + y^2 = 0
(x-6)^2 + y^2 = 36

This one is just the reverse process:

(x+7)^2 + y^2 = 49
x^2 + 14x + y^2 = 0
x^2 + y^2 = -14x
r^2 = -14r cosθ
r = -14 cosθ

Answer 2

thank you!

Answer 3

I mixed up x and y in the 1st one!

x^2+y^2 = 12y
x^2 - 12y + y^2 = 0
x^2 + (y-6)^2 = 36

Also, the 2nd one could just as well have been written r = 14cosθ. It would just draw the circle from the left, rather than from the right.