Let P Q be a focal chord of the parabola y 2 = 36 x of length 100 , making an acute angle with the positive x - axis. Let the ordinate of P be positive and M be the point on the line segment P Q such that P M : M Q = 3 : 1 . Then which of the following points does NOT lie on the line passing through M and perpendicular to the line P Q ?

Question

Let P Q be a focal chord of the parabola y 2 = 36 x of length 100 , making an acute angle with the positive x - axis. Let the ordinate of P be positive and M be the point on the line segment P Q such that P M : M Q = 3 : 1 . Then which of the following points does NOT lie on the line passing through M and perpendicular to the line P Q ?, - 6 , 45, 6 , 29, 3 , 33, - 3 , 43

MARKS App · Accepted Answer

We have been given the length of focal chord P Q = 100 . Length of focal chord at t = a t + 1 t 2 = 100 Where a = 9 t + 1 t = ± 10 3 ∴ t = 3 , 1 3 , - 3 , - 1 3 Since ordinate of P is + ve ∴ t = 3 or 1 3 ( t = 3 as slope of P Q is positive) ∴ M ( 21 , 9 ) Required line : y - 9 = - 80 60 ( x - 21 ) ⇒ 4 x + 3 y = 111 - 3 , 43 does not lie on line. Hence this is the correct option.

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