satellite spot beam oblique footprint

I am trying plot a satellite slant foot print with an oblique beam width of 2 degrees projected on the world map at the edges of the satellite's horizon visibility on Earth. If the satellite is at the Equator, and altitude is a variable, I expect to see the projection as a perfect truncated ellipse by the Earth horizon visibility contour on the East or West directions. Tried various projection methods and failed. Appreciate assistance.