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Line And Ellipse

Source: 2002 National High School Mathematics League, Exam One, Problem 4

March 13, 2020
conicsellipsegeometry

Problem Statement

Line x4+y3=1\frac{x}{4}+\frac{y}{3}=1 and ellipse x216+y29=1\frac{x^2}{16}+\frac{y^2}{9}=1 intersect at AA and BB. A point on the ellipse PP satisties that the area of △PAB\triangle PAB is 33. The number of such points is (A)1(B)2(C)3(D)4\text{(A)}1\qquad\text{(B)}2\qquad\text{(C)}3\qquad\text{(D)}4
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