Hello! In some problems with a parameter that can be solved graphically by depicting one circle and a hyperbola, and then analyzing the number of solutions, the circle touches the hyperbola at a point that belongs to the line x = y. Understanding this, you can find the coordinates of the intersection point by substituting y x in the equation. But how to prove that the hyperbola intersects with a circle at a point that belongs to the line x = y or -x = y? In general, I would like to know how to prove the symmetry of a hyperbola with respect to the line x = y or -x = y. Can you help me?