The locus of the mid points of the chords of the hyperbola x2 $-$ y2 = 4, which touch the parabola y2 = 8x, is :

Question

The locus of the mid points of the chords of the hyperbola x² $-$ y² = 4, which touch the parabola y² = 8x, is :

y³(x $-$ 2) = x²

x³(x $-$ 2) = y²

y²(x $-$ 2) = x³

x²(x $-$ 2) = y³

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