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JEE Main202120 Jul 2021Evening ShiftMathematicsParabolaActual

If the point on the curve y 2 = 6 x , nearest to the point 3 , 3 2 is ( α , β ) , then 2 ( α + β ) is equal to _________.

Correct answer

0

Step-by-step solution

We have, y 2 = 6 x Comparing with y 2 = 4 a x , we get a = 3 2 Let the point on parabola be P ≡ a t 2 , 2 a t ≡ 3 2 t 2 , 3 t . Normal at point P is t x + y = 3 t + 3 2 t 3 It passes through 3 , 3 2 , hence ⇒ 3 t + 3 2 = 3 t + 3 2 t 3 ⇒ t 3 = 1 ⇒ t = 1 Hence, P ≡ 3 2 , 3 = ( α , β ) Therefore, 2 ( α + β ) = 2 3 2 + 3 = 9

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