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High school math ellipse (speed!
The existence of point P on the ellipse makes the straight line PF 1 perpendicular to the straight line PF2.

F 1f2 is the hypotenuse, and the median line of the hypotenuse of a right triangle is equal to half of the hypotenuse.

(a > b > 0) the focus is on the x axis. If c < b, then point p should be inside the ellipse, but not on the ellipse. The shortest line segment from the point on the ellipse to the origin is B, so | op | = C ≥ B.