Fitting 2 arc, parabola, ellipse to 2 points and 2 slopes

This project is to create a function for 2 arcs, and or a parabola and or an ellipse: When you bid on this job please state if you will do the 2 arcs, parabola, ellipse of both, all etc. Function Inputs: start x start y start slope end x end y end slope x intersection along curve The function may need additional inputs such as start radius, end radius or ratio of the two radii, I don't know yet hopefully you can figure that out. Return: y value of x intersection along curve The resulting curve must NOT have reversal in curvature, it must be convex on one side of the curve and concave on the other for the entire length of the curve. If you can d it in VB.net that would be great but if you can write it clearly in another language I can probably convert it.