Identify the conic section $$$x^{2} - y^{2} = \left(x - y\right)^{2}$$$

Identify and find the properties of the conic section $$$x^{2} - y^{2} = \left(x - y\right)^{2}$$$.

The general equation of a conic section is $$$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$$$.

In our case, $$$A = 0$$$, $$$B = 2$$$, $$$C = -2$$$, $$$D = 0$$$, $$$E = 0$$$, $$$F = 0$$$.

The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = 0$$$.

Next, $$$B^{2} - 4 A C = 4$$$.

Since $$$\Delta = 0$$$, this is the degenerated conic section.

Since $$$B^{2} - 4 A C \gt 0$$$, the equation represents two distinct intersecting lines.

$$$x^{2} - y^{2} = \left(x - y\right)^{2}$$$A represents a pair of the lines $$$y = 0$$$, $$$y = x$$$A.

General form: $$$2 x y - 2 y^{2} = 0$$$A.

Factored form: $$$y \left(- x + y\right) = 0$$$A.

Graph: see the graphing calculator.