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

Question

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,

MARKS App · Accepted Answer

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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