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

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The locus of the mid-point of the line segment joining the focus of the parabola \( y^{2}=4 a x \) to a moving point of
\( \mathrm{P} \) the parabola, is another parabola whose directrix is:

W
(a) \( x=a \)
[JEE Main-2021]
(b) \( x=0 \)
(c) \( x=-\frac{a}{2} \)
(d) \( \frac{a}{2} \)
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