The locus of the mid-point of the line segment joining the focus to...

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The locus of the mid-point of the line segment joining the focus to a moving point on the parabola \( y^{2}=4 a x \) is another parabola with directrix:
[IIT-JEE (Screening) 2002]
\( \mathrm{P} \)
(a) \( x=-a \)
(b) \( x=-a / 2 \)
(c) \( x=0 \)
(d) \( x=a / 2 \)
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