Thread: Equation of sea shell type geometrical shape

I am a student of University of Dhaka, Faculty of Engineering and Technology. I have a problem to find out the resultant equation of sea shell type geometrical shape which is shown in my attachment JPEG file.

Equation of parabolic section : X^2 = 4 *f * (Y + f), where f = Focus of parabola.

Equation of Circular section : X^2 + Y^2 = f^2, where f= Radius of Circle.

Now problem is that to find out the general equation by combining this two curvature shown in attachment file.
If it is possible, please help me....