Let the tangents P Q and P R are drawn to y 2 = 4 a x from any point P on the line x + 4 a = 0 . The angle subtended by the chord of contact Q R at the vertex of the parabola y 2 = 4 a x is

Question

Let the tangents P Q and P R are drawn to y 2 = 4 a x from any point P on the line x + 4 a = 0 . The angle subtended by the chord of contact Q R at the vertex of the parabola y 2 = 4 a x is, π 4, π 3, π 2, π 6

MARKS App · Accepted Answer

Let, Q = a t 1 2 , 2 a t 1 and R = a t 2 2 , 2 a t 2 , then P = a t 1 t 2 , a t 1 + t 2 which lies on x + 4 a = 0 ⇒ a t 1 t 2 = - 4 a ⇒ t 1 t 2 = - 4 Now, the vertex of the parabola y 2 = 4 a x is the origin O 0,0 ⇒ slope of O Q = 2 t 1 & slope of O R = 2 t 2 ⇒ 2 t 1 × 2 t 2 = 4 t 1 t 2 = 4 - 4 = - 1 ⇒ O Q is perpendicular to O R ⇒ ∠ Q O R = 9 0 ∘ = π 2

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