F: the other focus of the planetary orbit.
S: Sun, or the center of gravitational force.
c: circle of radius = 2x(semimajor axis)
c' : hodograph of the velocity vector. generated by rotating the circle c 90 degrees clockwise(or anticlockwise, according to the assumed direction of orbital motion of the planet.) around S.
D: any point on c
d: perpendicular bisector of segment SD
P: location of the planet, intersection of line d and segment FD
The red ellipse: locus of P as D moves around c.
a: the line parallel to line d
B: intersection of c' and a
SB: line segment parallel to d, the tangent to the ellipse and its length proportional to the orbital speed.
F': center of the hodograph, generated by rotating F 90 degrees clockwise about S.
PP'(the blue arrow): parallel translation of SB with its tail onto P.
Drag D about the circle to see how the point P and the velocity vector moves.
Drag S out of the circle c to get the hyperbolic orbit, and try the tasks for the hyperbolic orbit as well.

show that the line d is tangent to the locus of P.

show that the locus of P is an ellipse.

Show that the product of length SB and of SD is constant.

Using Kepler's 2nd Law, show that SB is proportional to the orbital speed.

Show that SB is parallel to the velocity.

Show that the angles FSP and SF'B are equal.

Explain physically why the angles FSP and SF'B are equal, using the Kepler's 2nd Law and Newtons Law of Gravitation(i.e. the inverse square law).