1)

 The locus  of the mid-point of the line segment joining the focus to a moving point on the parabola, y2=4ax  is a conic . The equation of the directrix of that conic is 


A) y=a

B) x=a

C) y=0

D) x=0

Answer:

Option D

Explanation:

Let Q(h,k)  be the mid-point of the line  joining  the  focus F(a,0)  and variable point p(x0,y0).

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       (h,k)=(x0+a2,y02)

     h=x0+a2 and k=y02

      x0=2ha   and y0=2k

Since P(x0,y0) lies on parabola y2=4ax

          y20=4ax0(2k)2=4a(2ha)

     4k2=4a(2ha)k2=2a(ha2)

Which is equation  of parabola 

   y2=2a(xa2)

    Equation of directrix is given by

xa2=a2x=0