The triangle PQR of area A is inscribed in the parabola y 2 = 4 a x such that P lies at the vertex of the parabola and base QR is a focal chord. The numerical difference of the ordinates of the points

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The triangle PQR of area A is inscribed in the parabola y 2 = 4 a x such that P lies at the vertex of the parabola and base QR is a focal chord. The numerical difference of the ordinates of the points Q \& R is

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QR is a focal chord. ​ ⇒ R ( a t 2 , 2 a t ) Q ( t 2 a ​ , − t 2 a ​ ) ⇒ d = ​ 2 a t + t 2 a ​ ​ = 2 a ​ t + t 1 ​ ​ Now A = 2 1 ​ ​ a t 2 t 2 a ​ 0 ​ 2 a t − t 2 a ​ 0 ​ 1 1 1 ​ ​ = a 2 ​ t + t 1 ​ ​ ⇒ 2 a ​ t + t 1 ​ ​ = a 2 A ​ ​

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