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Analytic Geometry

Source: 1998 National High School Mathematics League, Exam One, Problem 15

March 9, 2020
conicsparabolaanalytic geometrygeometry

Problem Statement

Parabola y2=2pxy^2=2px, two fixed points A(a,b),B(−a,0)(ab≠0,b2≠2pa)A(a,b),B(-a,0)(ab\neq0,b^2\neq 2pa). MM is a point on the parabola, AMAM intersects the parabola at M1M_1, BMBM intersects the parabola at M2M_2. Prove: When MM changes, line M1M2M_1M_2 passes a fixed point, and find the fixed point.
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