Originally Posted by

**bsev** Thanks **SammyS**!

I know I wrote it is a parabola, but I did so only because it looked like one.

Still, do you think there is a way to examine whether or not it is a parabola?

I'm convinced there is a way to show that this is a parabola.

I haven't come up with an **easy** way.

One idea:

Find the point of intersection (x_1, y_1) for two lines, one with r=R, the other with r=R+ε . Take the limit as ε → 0. That should be the point at which the line with r=R is tangent to the unknown curve.

To be thorough, do the same with r=R-ε.

That's a start. The result should be consistent with the previous analysis which assumed a parabolic shape.

BTW: I found another mistake in my **post #5** above.

The equation for the tangent line should be: $\displaystyle x=(-2a\,y_0)y+\,a{y_0}^2\,,$ because the x-intercept is $\displaystyle a{y_0}^2\,.$