how to test symmetric over the line pi/2 with the equation r=6/(1+sintheta)

Question

anonymous · Answer

$$r=6\sin \theta$$
Multiply both sides by r
$$r^2 = 6 r \sin \theta$$

transform to rectangular coordinates.
$$x^2+y^2 = 6y$$

$$x^2+y^2-6y+9=9$$
$$x^2+(y-3)^2=9$$

A circle with center (0,3) and radius 3 is symmetric about the line x=0 (y-axis)

anonymous · Answer

wait, how did you get 6 sin $$\theta$$
when the equation is  $$6 \div 1 +\sin \theta$$
and they want to test algebraically

anonymous · Answer

So, YOU CAN do TAT!

anonymous · Answer

i use the method of replacing $$(r,\theta) \to (-r,-\theta) $$
the i get the final answer but it doesn't seem right because it is $$r=6\div1-\sin \theta $$
it isn't the same, so I am confused even though I know it must be symmetric. because the graph is a parabola

anonymous · Answer

@dpaInc a medal

anonymous · Answer

@Rohangrr , she's right... the equation is |dw:1337410988731:dw|