Three Dimensional Geometry

The given equation is axy+by=cy.
We can simplify this to:
ax+bz=c
This equation represents a plane. The key characteristic of this plane is its orientation in space.
Since there is no specific term dealing with the y-coordinate in the rearranged equation ax+bz=c, this plane is parallel to the Y-axis.
Thus, it is a plane that is perpendicular to the ZX-plane or could coincide with the ZX-plane itself.
In simpler terms, the ZX-plane is defined where y=0, and any plane parallel to it or identical will have no effect from changes in the y-coordinate.