Max S of the trapezoid with an ellipse

  • 公開日時: 2018/11/04 17:35
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Let $F_1,\ F_2$ be foci of the ellipse $\displaystyle E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ where $a,\ b\ (a>b)$ are positive constants.Drop perpendiculars $F_1H_1,\ F_2H_2$ from $F_1,\ F_2$ to a tangent line drawn at a point of tangency on the ellipse in the first quadrant. Find the maximum value of the trapezoid $F_1H_1H_2F_2,$ and also the coordinate of the point of tangency. \ Proposed by me on May 6, 2010