A Circumcircle of Maximal Area

Problem

The ellipse C:x29+y23=1C:\dfrac{x^2}9+\dfrac{y^2}3=1 has left vertex AA. A line ll through the point B(1,0)B(1,0) meets CC at two points PP and QQ. Let NN be the circumscribed circle of △APQ\triangle APQ.

1. When ll is perpendicular to the xx-axis, find the equation of the circle NN. 2. Find the maximum area of the circle NN.

Answer

Solution

Difficulty8/10
TopicsCircles, conic sections, AM-GM, analytic geometry, Vieta's Formulas

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