An Area Range of a Fixed Chord

Problem

Let A,BA,B be two points on the ellipse x28+y22=1\dfrac{x^2}8+\dfrac{y^2}2=1 with chord length ∣AB∣=83|AB|=\dfrac 83. Find the range of the area of △AOB\triangle AOB, where OO is the origin.

Answer

Solution

Difficulty7/10
TopicsExtrema, Affine Transformation, conic sections

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