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Coordinates of the vertices \( B \) and \( C \) of a triangle \( A B C \) are \( (2,0) \) and \( (8,0) \) respectively. The vertex \( A \) is varying in such a way that \( 4 \tan \frac{B}{2} \cdot \tan \frac{C}{2}=1 \). Then locus of \( A \) is
\( \mathrm{P} \)
(A) \( \frac{(x-5)^{2}}{25}+\frac{y^{2}}{16}=1 \)
(B) \( \frac{(x-5)^{2}}{16}+\frac{y^{2}}{25}=1 \)
(C) \( \frac{(x-5)^{2}}{25}+\frac{y^{2}}{9}=1 \)
(D) \( \frac{(x-5)^{2}}{9}+\frac{y^{2}}{25}=1 \)
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