Tangents are drawn from the point ( − 1 , 2 ) to the parabola y 2 = 4 x . The length of the intercept made by the line x = 2 on these tangents is

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Equation of pair of tangent is ​ S S 1 ​ = T 2 ​ ⇒ ( y 2 − 4 x ) ( 8 ) = 4 ( y − x + 1 ) 2 ​ ⇒ y 2 − 2 y ( 1 − x ) − ( x 2 + 6 x + 1 ) = 0 ​ Put x = 2 ​ ⇒ y 2 + 2 y − 17 = 0 ​ ⇒ ∣ y 1 ​ − y 2 ​ ∣ = 6 2 ​ ​

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