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Let tangents P Q and P R are drawn from the point P - 2,4 to the parabola y 2 = 4 x . If S is the focus of the parabola y 2 = 4 x , then the value (in units) of R S + S Q is equal to

Correct answer

22

Step-by-step solution

Let, Q = t 1 2 , 2 t 1   &   R = t 2 2 , 2 t 2 , then P = t 1 t 2 , t 1 + t 2 = - 2,4 ⇒ t 1 t 2 = - 2     &     t 1 + t 2 = 4 Now, Q S = 1 + t 1 2 ,   R S = 1 + t 2 2 ⇒ Q S + R S = 2 + t 1 2 + t 2 2 = 2 + t 1 + t 2 2 - 2 t 1 t 2 = 2 + 4 2 - 2 - 2 = 2 + 16 + 4 = 22 units

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