Coordinates of the vertices B & C are ( 2 , 0 ) and ( 8 , 0 ) respectively. The vertex ' A ' is varying in such a way that 4 tan 2 B tan 2 C = 1 . If the locus of ' A ' is an e

Question

Coordinates of the vertices B & C are ( 2 , 0 ) and ( 8 , 0 ) respectively. The vertex ' A ' is varying in such a way that 4 tan 2 B ​ tan 2 C ​ = 1 . If the locus of ' A ' is an ellipse then the length of its semi major axis is

TestHub · Accepted Answer

4 tan 2 B ​ tan 2 C ​ = 1 ​ ⇒ s ( s − b ) s ( s − c ) ( s − c ) ( s − a ) ( s − a ) ( s − b ) ​ ​ = 4 1 ​ ​ ⇒ s s − a ​ = 4 1 ​ ⇒ a 25 − a ​ = 3 5 ​ ⇒ b + c = 3 5 ​ × 6 = 10 ​ ( ∵ a = BC = 6 ) ​ ∴ Locus of A is ​ 25 ( x − 5 ) 2 ​ + 16 y 2 ​ = 1 ​

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