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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