Reflection of a Point Object in an Arbitrary Curved Mirror

In this work, I have derived the equation of the curve obtained on reflection of a point object in an arbitrary curved mirror if the object and the mirror are placed on the 2D Cartesian plane. I have used only the basic laws of reflection of classical geometric optics and elementary coordinate geometry. Several examples are provided and compared with Gaussian optics. We also see how the equations reduce to the standard mirror formula under the paraxial approximation.