The locus of the mid points of all chords of the parabola y<sup>2</sup> = 4x, which are drawn through its vertex, is
The vertex is (0, 0). Any other point on \(y^2 = 4x\) is \((t^2, 2t)\).
The midpoint of the chord is \((h, k) = \left(\frac{t^2}{2}, t\right)\).
From \(k = t\), we get \(h = \frac{k^2}{2}\), so \(k^2 = 2h\).
Locus: \(y^2 = 2x\)
Answer: (B)
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