x = Cx + a * cos(ang);
y = Cy + b * sin(ang);
Cx, Cy are cords of center. ang is angle in radians. a is half of width, b is half of height.
If I change values of ang, I get different points on circumference of ellipse.
Below is the path which I get with above equation.

But instead of this elliptical shape, I want something like half ellipse, something like concave mirror. Even if we stretch both of its end to infinity, they should not form elliptical shape.

Can somebody provide me polar equations for second curve. I am very bad at digital drawing but you can imagine thas as concave mirror.