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Parabola

Source: 2003 National High School Mathematics League, Exam One, Problem 3

March 16, 2020
conicsparabolageometryperpendicular bisector

Problem Statement

Line passes the focal point FF of parabola y2=8(x+2)y^2=8(x+2) with bank angle of 60∘60^{\circ} intersects the parabola at A,BA,B. Perpendicular bisector of ABAB intersects xx-axis at PP, then the length of PFPF is (A)163(B)83(C)1633(D)83\text{(A)}\frac{16}{3}\qquad\text{(B)}\frac{8}{3}\qquad\text{(C)}\frac{16}{3}\sqrt3\qquad\text{(D)}8\sqrt3
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