设△PF1F2的内切圆与F1F2,F2P,PF1的切点分别是D,E,G,圆心的横坐标是x0,则
|PF1|-|PF2|
=|F1G|-|F2E|
=|F1D|-|F2D|
=x0+c-(c-x0)
=2x0=2a,
∴x0=a.