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…

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

  1. 3x2+2y-6=0
  2. 2x2-3y+9=0
  3. 3x2-2y-6=0
  4. 2x2+3y-9=0

Solution

Mid point M=t,3

mAB=-3t

Perpendicular bisector of AB is 

y-3=t3x-t

So, C=0, 3-t23

Let P be h, k

h=t2; k=3-t26

⇒k=3-4h26

⇒2x2+3y-9=0

Asked in: JEE Main 2021 (27 Aug Shift 1)

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