The locus of the midpoint of the segment joining the focus to a moving point on the parabola \( ...

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The locus of the midpoint of the segment joining the focus to a moving point on the parabola \( y^{2}=4 a x \) is another parabola with directix
(A) \( y=0 \)
(B) \( x=-a \)
(C) \( x=0 \)
(D) none of these
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