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B and C are the vertex of a triangle ABC...

B and C are the vertex of a triangle ABC with coordinate (2 , 0) and (8 , 0) respectively. Another vertex A moves in such a way that it satisfies the relation `4 " tan" (B)/(2) "tan" (C)/(2) = 1 `. If the equation of locus of A is `(x - 5)^(2)/5^2+ (y^(2))/(k^(2)) = 1 ` , then the value fo k is _

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