Identify the conic section $$$- 180 x^{2} - 30 x + 12 = 0$$$

Identify and find the properties of the conic section $$$- 180 x^{2} - 30 x + 12 = 0$$$.

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, $$$A = 180$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = 30$$$, $$$E = 0$$$, $$$F = -12$$$.

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 parallel lines.

$$$- 180 x^{2} - 30 x + 12 = 0$$$A represents a pair of the lines $$$x = - \frac{5 + \sqrt{265}}{60}$$$, $$$x = \frac{-5 + \sqrt{265}}{60}$$$A.

General form: $$$180 x^{2} + 30 x - 12 = 0$$$A.

Factored form: $$$\left(60 x + 5 + \sqrt{265}\right) \left(60 x - \sqrt{265} + 5\right) = 0$$$A.

Graph: see the graphing calculator.