Just prove that the normal PQ of point P bisects ∠F 1PF2. (Normal refers to a straight line that passes through a point on the graph and is perpendicular to the tangent of that point. For example, if PT is tangent and PQ⊥PT passes through P, then PQ is called the normal of point P).

Let P(x0, y0), obviously y≠0 (that is, p is not on the X axis), and make a straight line PQ to make Q on the X axis.

According to the inverse theorem of the angular bisector theorem, it can be proved that PQ is the bisector of ∠ F 1/QF2 or PF 1*QF2=PF2*QF 1

So please calculate the length of the four line segments by yourself. The amount of calculation is a bit large, but it is not difficult. It's a mess here Do it yourself