Identify the conic section $$$y^{2} + \left(2 - y\right)^{2} = -4$$$

Identify and find the properties of the conic section $$$y^{2} + \left(2 - y\right)^{2} = -4$$$.

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, $$$A = 0$$$, $$$B = 0$$$, $$$C = 2$$$, $$$D = 0$$$, $$$E = -4$$$, $$$F = 8$$$.

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, $$$B^{2} - 4 A C = 0$$$.

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

Since $$$B^{2} - 4 A C = 0$$$, the equation represents two nonreal lines.

$$$y^{2} + \left(2 - y\right)^{2} = -4$$$A represents two nonreal lines.

General form: $$$2 y^{2} - 4 y + 8 = 0$$$A.