How to detect if an ellipse intersects(collides with) a circle

Question

I want to improve a collision system.

Right now I detect if 2 irregular objects collide if their bounding rectangles collide.

I want to obtain the for recta

Answer 1

This isn't that hard. user168715's answer is generally right, but doing calculus isn't necessary. Just trigonometry.

Find the angle between the center of the two objects. Using this you can find the closest point to the circle's center on the ellipse using the polar-form:

(Taken from Wikipedia article on Ellipses)

Now compare the distance between the two object centers, subtracting the ellipse radius and circle radius.

Maybe I'm missing something; maybe ArcTan/Cos/Sin are slow -- but I don't think so, and there should be fast-approximations if needed.