Identify the conic section $$$\frac{x^{2}}{2} - 6 = y$$$

Identify and find the properties of the conic section $$$\frac{x^{2}}{2} - 6 = y$$$.

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, $$$A = \frac{1}{2}$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = 0$$$, $$$E = -1$$$, $$$F = -6$$$.

The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = - \frac{1}{2}$$$.

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

Since $$$B^{2} - 4 A C = 0$$$, the equation represents a parabola.

To find its properties, use the parabola calculator.

$$$\frac{x^{2}}{2} - 6 = y$$$A represents a parabola.

General form: $$$\frac{x^{2}}{2} - y - 6 = 0$$$A.

Graph: see the graphing calculator.