Cone, plane, parabola

ValeryOchkov · ‎Jan 08, 2020

With cone? plane and ellipse all is cleare.

Thanks!

And what about a parabola?

I know O-F - can I calculate the theta?

Can the cone axis goes through the focus of the parabola?

Werner_E · ‎Jan 08, 2020

Same answers (no to both questions) as in the other thread, same way to see/prove it - Dandelin sqpere - there is only one in case of a parobola and it still touches the plane at the focal point of the parabola which can't be on the axis (as we would have a circle as intersection in that case and not a parabola.

With given plane, O and F you can put a Dandelin-sphere of any radius touching the plane in F. Depending on the radius of the sphere you get cones with different angles.

Your angle theta can be simply calculated by theta=arctan(OF/r) when r is the radius of the Dandelin-sphere which you can freely chose.