Let P(x1, y1) be the point of incidence of light. Let OP be the incident ray and PI be the reflected ray.
Find the slope of the tangent to the hyperbola at P. And from that find the slope of the normal at P.
The normal is the angle bisector of OPI.
Find the equation of OP and PI. From that find the equation of the angle bisector of angle OPI. Find the slope of the angle bisector.
Equate it with that of the normal. You will get a relation between x1 and y1. Substitute this in the equation of the hyperbola to find the co-ordinates of P.