Two mutually perpendicular tangents of the parabola y 2 = 4 a x at the points Q 1 and Q 2 on it meet its axis in P 1 and P 2 . If S is the focus of the parabola, then the value of 1 S P 1 + 1 S P 2 - 1 is equal to

Question

Two mutually perpendicular tangents of the parabola y 2 = 4 a x at the points Q 1 and Q 2 on it meet its axis in P 1 and P 2 . If S is the focus of the parabola, then the value of 1 S P 1 + 1 S P 2 - 1 is equal to, a 4, a 2, a, 2 a

MARKS App · Accepted Answer

Let Q 1 = a t 1 2 , 2 a t 1 & Q 2 = a t 2 2 , 2 a t 2 are points of contact of the tangents passing through P 1 & P 2 respectively. ⇒ P 1 = - a t 1 2 , 0 & P 2 = - a t 2 2 , 0 ⇒ P 1 S = a + a t 1 2 & P 2 S = a + a t 2 2 ⇒ 1 P S 1 + 1 P S 2 = 1 a + a t 1 2 + 1 a + a t 2 2 = 1 a + a t 1 2 + 1 a + a - 1 t 1 2 = 1 a

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