Area of circle, Lol

Geometry Level 5

\[\large P \equiv 16x^{2} - 24xy + 9y^{2} - 180x +10y + 625\]

If the center of a circle lies on latus rectum of the conic \(P=0\) and the directrix of the conic \(P=0\) is the tangent to this circle, then find the area of this circle.

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