Answer is (A) xy - 4bx + 3ay = 0
Let point of contact of tangent P is (α, λα3) through point A(α, β) and let this tangent cuts the curve again at point B (β, λβ3).
Slope of PB = Slope of tangent at point P
Slope of PA = Slope of tangent at point P
Hence, locus of B is xy - 4bx + 3ay = 0.