Pre calculus question

Question

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line theta = pi/2. (Select all that apply.)

r^2 = 4 sin (theta)

symmetric with respect to the polar axis

symmetric with respect to the pole

symmetric with respect to the line theta = pi/2

not symmetric with respect to any of these

Answer 1

r^2 = 4rsinT

x^2+y^2 =4y

x^2 +y^2 -4y +4 = 4

x^2 + (y-2)^2 = 2^2

is a circle, with center (0,2) radius = 2

it's symmetric about any straight line through the center, such as y=2

or x=0 which is the same as Theta=pi/2