Which of the following is the Cartesian equation for the polar equation r = -6 sin (θ)?

Question

Which of the following is the Cartesian equation for the polar equation r = -6 sin (θ)?

A	x2 + y2 = 9
B	x2 + (y - 3)2 = 36
C	x2 + (y + 3)2 = 9
D	(x - 1)2 + y2 = 9

Answer 1

The way to move between polar and cartesian coordinates is through x=rcos(θ) and y=rsin(θ).

Thus, r = -6sin(θ) = -6y/r ⇒ r² = x² + y² = -6y ⇒ x² + y² + 6y = 0 ⇒ x² + (y+3)² - 9 = 0