Question

Take any point on the parabola ( left(a t^{2}, 2 a tright) )
Therefore the mid point ( (h, k)=left(frac{a t^{2}+a}{2}, frac{2 a t+0}{2}right) )
( 2 h=aleft(t^{2}+1right), a t=k )
( 2 h=aleft(frac{k^{2}}{a^{2}}+1right) )
So.locus is ( 2 x a=y^{2}+a^{2} )
( y^{2}=2 a(x-a / 2) )
Direction ( : x=frac{a}{2}+frac{a}{2} )
( =0 ) or ( y ) axis
Hence C is the correct answer.

# The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y? = 4ax is another parabola with directrix (a) x = -a (b) x=- (c) x = 0 (d) x=9

Solution