The locus of the mid-point of the l...
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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

JEE/Engineering Exams
Maths
Solution
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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.
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