If the common tangents of hyperbola x^2/...

If the common tangents of hyperbola `x^2/4-y^2/1=lambda` and the parabola `y^2=4x` cuts the coordinate axis at A and B, then locus of midpoint of AB is (A) `y^2 = -2x` (B) `2y^2 =-x` (C) `x^2 - y^2 =2` (D) `y^2 =x`

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