Let A be a fixed point ( 0 , 6 ) and B be a moving point ( 2 t , 0 ) . Let M be the mid-point of A B and the perpendicular bisector of A B meets the y - axis at C . The locus of the mid-point P of MC

Question

Let A be a fixed point ( 0 , 6 ) and B be a moving point ( 2 t , 0 ) . Let M be the mid-point of A B and the perpendicular bisector of A B meets the y - axis at C . The locus of the mid-point P of MC is

TestHub · Accepted Answer

Mid point M = t , 3 m AB = - 3 t Perpendicular bisector of AB is y - 3 = t 3 x - t So, C = 0 , 3 - t 2 3 Let P be h , k h = t 2 ; k = 3 - t 2 6 ⇒ k = 3 - 4 h 2 6 ⇒ 2 x 2 + 3 y - 9 = 0

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