How to Determine Ellipse Axes from Cone Geometry?

[femas]

Hi,

If the cone is cut with a plane such that an ellipse has been formed. Let's say the major axis is 'a' and the minor axis is 'b'.

Is there a way to find a and b from the geometry instead of getting them from the quadratic equation.

 

[Eynstone]

The inclination of the plane would give the ratio a:b & its distance from the vertex of the cone would give a. I would prefer to do this trigonometrically.

 

[femas]

Thank you ... But can you give me an example.

 

[slider142]

The distance of the plane from the vertex of the cone as measured along the axis of the cone and the slope of the cone determines the semi-minor axis of the ellipse, while the inclination of the plane together with that distance determines the semi-major axis.