I'm convinced there is a way to show that this is a parabola.
Originally Posted by bsev
I haven't come up with an easy way.
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.That's a start. The result should be consistent with the previous analysis which assumed a parabolic shape.
To be thorough, do the same with r=R-ε.
BTW: I found another mistake in my post #5 above.
The equation for the tangent line should be: because the x-intercept is