Locus of the middle points of all chords of the parabola \( y^{2}=4 x \) which are drawn through...

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Locus of the middle points of all chords of the parabola \( y^{2}=4 x \) which are drawn through the vertex, is
(A) \( y^{2}=8 x \)
(B) \( y^{2}=2 x \)
(C) \( x^{2}+4 y^{2}=16 \)
(D) \( x^{2}=2 y \)
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