## ellipse detection in cone

Hello everyone,

this is my question:

Given a positive fully known cone and an ellipse which we only know its focus and excentricity, if the ellipse is contained in the cone, does the family of all the ellipses contained in the cone have one degree of freedom (the rotation of this ellipse around the cone axis) or it has more than one? If so, is it possible to calculate the homogeneous transformation of the center (position and orientation) of the ellipse relative to a fixed point on the cone (depending on the degree of freedom, of course)?

Thanks everyone, hope everything in my question is clear.

Josep