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Ellipse Problem

Source: 1999 National High School Mathematics League, Exam One, Problem 14

March 10, 2020
conicsellipseanalytic geometry

Problem Statement

Given A(−2,2)A(-2,2), and BB is a moving point on ellipse x225+y216=1\frac{x^2}{25}+\frac{y^2}{16}=1. FF is the left focal point of the ellipse, find the coordinate of BB when ∣AB∣+53∣BF∣|AB|+\frac{5}{3}|BF| takes its minumum value.
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