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Question

The locus of the mid-point of the line segment joining the focus ot a moving point on the parabola y2 = 4ax is another parabola with directrix


  1. x=a2

  2. x = - a

  3. x = 0 

  4. x=a2


Solution

The correct option is C

x = 0 


S=(a,0),P(at2,2at).If(h,k) be midpoint, then 2h=a(1+t2),2k=2at or k=at
 2x =a (1+y2a2 )or y2=2a(xa2 )or Y2=4AX
 Directrix is X = A or x a2=2a4 or x = 0.

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