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Source: 1985 National High School Mathematics League, Exam One, Problem 2

February 23, 2020
analytic geometrygeometry3D geometryconicsparabola

Problem Statement

PQPQ is a chord of parabola y2=2px(p>0)y^2=2px(p>0) and PQPQ pass its focus FF. Line ll is its directrix. Projection of PQPQ on ll is MNMN. The area of curved surface that PQPQ rotate around ll is S1S_1, the area of spherical surface of the ball with diameter of MNMN is S2S_2, then (A)S1>S2(B)S1<S2(C)S1≥S2(D)\text{(A)}S_1>S_2\qquad\text{(B)}S_1<S_2\qquad\text{(C)}S_1\geq S_2\qquad\text{(D)} Not sure
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