Answer is (A) ayz + bzx + cxy = xyz
Let the equation to the plane be
x/α + y/β + z/γ = 1 ⇒ a/α + b/β + c/γ = 1
(since the plane passes through a, b and c).
Now the points of intersection of the plane with the coordinate axes are A(α, 0, 0), B(0, β, 0) and C(0, 0, γ ).
Equations to planes parallel to the coordinate planes and passing through A, B and C are x = α, y = β and z = γ . Therefore, the locus of the common point is
a/x + b/y + c/z = 1 (by eliminating α, β and γ from above equation)