Creating an automatic tangent line from origin to a curve

I'd like to make a diagram showing a polar curve for a paraglider with a line from origin that touch the polar according to enclosed drawing.
This is fairly easy to make manually for a single setup, but I'd like to be able to move the polar (both in x and y direction) and have the tangent follow it automatically.
Depending on the position of the polar the intersection point will vary of course. If possible I'd like it to display the x/y value of the intersection point

Basically it's solving 2 equations, the curve:
Y1=Ax^2 + Bx + C
and the line
Y2= Cx + D (Where D has to be 0/zero to have the line go through x,y=0,0)

And then somehow solving for a given curve where the point X1=X2 and Y1=Y2 is and thus finding C

Any good ideas?

Polar curve.JPG