Normals drawn to y 2 = 4 a x at the points where it is intersected by the line y = m x + c intersected at P . Coordinates of foot of the another normal drawn to the parabola from the point P is

Question

Normals drawn to y 2 = 4 a x at the points where it is intersected by the line y = m x + c intersected at P . Coordinates of foot of the another normal drawn to the parabola from the point P is, a m 2 , - 2 a m, 9 m , - 6 a m, a m 2 , - 2 a m, 4 a m 2 , - 4 a m

MARKS App · Accepted Answer

Let y = m x + c , intersect y 2 = 4 a x at A a t 1 2 , 2 a t 1 and B a t 2 2 , 2 a t 2 . Then, 2 t 1 + t 2 = m ⇒ t 1 + t 2 = 2 m Let the foot of another normal be C a t 3 2 , 2 a t 3 Then, t 1 + t 2 + t 3 = 0 t 3 = t 1 + t 2 = - 2 m Thus, other foot is 4 a m 2 , - 4 a m Hence, option (d) is correct.

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