The locus of the midpoint of the focal distance of a variable point...

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The locus of the midpoint of the focal distance of a variable point moving on the parabola \( y^{2}=4 a x \) is a parabola whose
\( \mathrm{P} \)
(1) latus rectum is half the latus rectum of the original
W parabola
(2) vertex is \( (a / 2,0) \)
(3) directrix is \( y \)-axis
(4) focus has coordinates \( (a, 0) \)
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