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On an ellipse x^2 64 + y^2 9 =1 , tangents drawn at P₁, P₂, P₃ . . P_n intersects the major axis at T₁, T₂, T₃ . T_n respectively. if the value of _ i=1 ^n Arca ( P_i T₁ S ) Area ( P_i T_i S^ ) (P₁ T_i )^2 =18 , then n is equal to

Correct answer

8

Step-by-step solution

aligned & Area of P₁ S T₁= 1 2 P₁ T₁ S M & Area of P₁ T₁ S^ = 1 2 P₁ T₁ S^ M^ & Area ( P ₁ ~T ₁ ~S ) Area ( P ₁ ~T ₁ ~S ^ ) ( P ₁ ~T ₁ )^2 = 1 4 SM ~S ^ M ^ = b ^2 4 & _ i=1 ^n Area ( PiTiS ) Area ( PiTiS ^ ) ( PiTi )^2 = n b^2 4 & n b^2 4 =18 & n = 4 18 9 =8 & n =8 aligned

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