Leave text as is. (You may add that F1 is the north pole or that the sum of the distances
from Q to F1 and F2 equals the radius of the circle - same definition as in the plane.)

Let there be a fixed circle C with center F1 (north pole) on a sphere.

Let there be a fixed point F2 inside the circle, not coincide with F1.

Let P be a point on C.

Let t be a line perpendicular to line[P, F2] and intersect midpoint[P, F2]

Let Q be the intersection[line[F1,P], line[t]]

As Q move about, Q traces out an ellipse, and t is its tagent at Q.

Note: t is a great circle. F1 and F2 are the foci.

Also, distance[Q, F1]+distance[Q, F2] equals the radius of the circle. This is similar to the definition of ellipse in the plane.