topic Re: Cone, plane, parabola in PTC Mathcad
https://community.ptc.com/t5/PTC-Mathcad/Cone-plane-parabola/m-p/643422#M188493
<P>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.</P>
<P>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.</P>
<P>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.</P>
<P> </P>Wed, 08 Jan 2020 20:09:20 GMTWerner_E2020-01-08T20:09:20ZCone, plane, parabola
https://community.ptc.com/t5/PTC-Mathcad/Cone-plane-parabola/m-p/643419#M188491
<P>With cone? plane and ellipse all is cleare.</P>
<P>See please <A href="https://community.ptc.com/t5/PTC-Mathcad/Cone-plane-ellipse/m-p/642807" target="_self">cone, plane, parabola</A> </P>
<P>Thanks!</P>
<P>And what about a parabola? </P>
<P>I know O-F - can I calculate the theta?</P>
<P><FONT style="background-color: #ffffff;">Can the cone axis goes through the focus of the parabola?</FONT></P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="Cone-parabola.png" style="width: 222px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22519i773B7E0895BF94F8/image-size/medium?v=v2&px=400" role="button" title="Cone-parabola.png" alt="Cone-parabola.png" /></span></P>Wed, 08 Jan 2020 19:49:46 GMThttps://community.ptc.com/t5/PTC-Mathcad/Cone-plane-parabola/m-p/643419#M188491ValeryOchkov2020-01-08T19:49:46ZRe: Cone, plane, parabola
https://community.ptc.com/t5/PTC-Mathcad/Cone-plane-parabola/m-p/643422#M188493
<P>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.</P>
<P>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.</P>
<P>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.</P>
<P> </P>Wed, 08 Jan 2020 20:09:20 GMThttps://community.ptc.com/t5/PTC-Mathcad/Cone-plane-parabola/m-p/643422#M188493Werner_E2020-01-08T20:09:20Z