Convert the conic equation from regular coordinate systems to the polar equivalent using the specifics below?

Keep in mind the idea is to start with the rectangular equation format (cartesian?) and then convert that to polar.

It's 3 parts, an ellipse, a parabola, and a hyperbola. I'm starting with the ellipse and haven't been able to figure it out.

Ellipse problem: "Find a polar equation for an ellipse that has foci (0, +-3) and vertices (0,+-5)."

As far as I'm aware we're using a horizontal ellipse equation so (x^2/b^2) + (y^2/a^2) = 1. Given the provided info, a = 5 and c = 3. Using given relationship for ellipses: c = sqrt(a^2 - b^2) I found b = 4.

This gives the equation (x^2/4^2) + (y^2/5^2) = 1. I don't know where to go from here in the process of converting this equation to polar. I know that x=rcos(0) and y=rsin(0) and r^2 = x^2 + y^2. Note that 0 is place for theta. Substituting for x and y gives me the equation...

(r^2cos^2(0)/16) + (r^2sin^2(0)/25) = 1. My algebra is spotty in this scenario so I'm not sure what to do with the 16 and 25 (if I multiply by 16 to get rid of it what happens to the 25? does it become 9?) and I don't really have any idea of what the end result should look like either...

I'm mainly looking for help with this problem because I think it'll guide me in solving the parabola and hyperbola but here are the specifics for those as well in case anyone is feeling generous or something.

Parabola Problem: "find a polar equation for a parabola that has its vertex at the origin and the Directrix y=-10"

Hyperbola Problem: "find a polar equation for a hyperbola that has vertices (0,+-6) and asymptotes y=+-(1/3)x