Coordinates

Geometry Level 5

Coordinates of the vertices \(B\) and \(C\) of a triangle \(ABC\) are \((2,0)\) and \((8,0)\) respectively. The vertex \(A\) is varying in such a way that :

\(4tan\dfrac { B }{ 2 } tan\dfrac { C }{ 2 } = 1\)

The locus of \(A\) is an ellipse. Then find out value of the product of the semi-major and semi-minor axis

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