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tangent to ellipse, triangle has minimal area

Source: VJIMC 1996 1.1

October 12, 2021
geometryconicsellipseintegrationcalculus

Problem Statement

On the ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 find the point T=(x0,y0)T=(x_0,y_0) such that the triangle bounded by the axes of the ellipse and the tangent at that point has the least area.
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