Parabola construction on a sphere
Drag points B and C (may be inside the sphere and hard to see the labels). These points control the inclination of the great circle that serves as a directirx.
Drag the blue focus point F (again, label may be inside the sphere).
Drag the green point D (this drives the locus point on the parabola).
One dashed line is perpendicular to the directirx, and the other is the perpendicular bisector of the focus F and the point on the directrix D.