What does underlined part mean in high school mathematics? Why can it be transformed into a relationship with the directrix?

Since F is the focus, BF=B'B, AM=A'A, AB=A'A+B'B, and M is the midpoint of AB,1/2ab =1/2 (a 'a+b 'b).

Because MN, AA', BB' are perpendicular to A'B', and M is the midpoint of AB, Mn =1/2 (AA'+BB') =1/2ab, and the median line on the hypotenuse of a right triangle is equal to half of the hypotenuse, so ABN is a right triangle and the angle anB is 90 degrees, so AN is perpendicular to BN.

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