Identify type of conic and more

[brutalmouse]

Identify type of conic and more...

Homework Statement

Identify the type of conic, find the vertices, the foci, directrix, and asymptotes (if they exist) for the equation e=45/(10+9sin(θ))

Homework Equations

As far as equations I don't know of any to help me find which type of conic, or any characteristics of this.

The Attempt at a Solution

Graphing in polar mode, I find that it is an ellipse.
I think we have to convert it from a polar equation into Cartesian coordinates.

 

[haruspex]

I assume e is what's normally written as r in polar.
Multiply out the equation. Then try rearranging it so that when you square both sides every occurrence of r is either as r² or as r sinθ.