Chord joining two distinct points P a , 4 b and Q c , - 16 b (both are variable points) on the parabola y 2 = 16 x always passes through a fixed point α , β . Then, which of the following statements is correct?

Question

Chord joining two distinct points P a , 4 b and Q c , - 16 b (both are variable points) on the parabola y 2 = 16 x always passes through a fixed point α , β . Then, which of the following statements is correct?, α + β = 2, α - β = 4, α + β = 8, α = β

MARKS App · Accepted Answer

Let, P = a , 4 b = 4 t 1 2 , 8 t 1 & Q = c , - 16 b = 4 t 2 2 , 8 t 2 ⇒ t 1 = b 2 and t 2 = - 2 b ⇒ t 1 t 2 = - 1 ⇒ Chord P Q is a focal chord that passes through the focus ⇒ α , β = 4,0

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