Let P=(x, y). First, find the right focus coordinate of the ellipse: (1, 0).

Then the midpoint coordinates of PF2 ((x+ 1)/2, y/2).

Also note that the coordinate of this midpoint is (u, v). Then x=2u+ 1 and y=2v. Substitute into elliptic equation to get

(2u+ 1)^2/4+(2v)^2/3= 1.

that is

(u+ 1/2)^2+v^2/(3/4)= 1.

This is the motion trajectory equation of the midpoint in PF2.

As can be seen from the equation, this trajectory is an ellipse with the center at (-1/2,0), the semi-major axis at1and the semi-minor axis at 3/4.