Identify the conic section $$$\frac{\left(x - 2\right)^{2}}{16} - 3 = 0$$$

Identify and find the properties of the conic section $$$\frac{\left(x - 2\right)^{2}}{16} - 3 = 0$$$.

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, $$$A = \frac{1}{16}$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = - \frac{1}{4}$$$, $$$E = 0$$$, $$$F = - \frac{11}{4}$$$.

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.

$$$\frac{\left(x - 2\right)^{2}}{16} - 3 = 0$$$A represents a pair of the lines $$$x = 2 - 4 \sqrt{3}$$$, $$$x = 2 + 4 \sqrt{3}$$$A.

General form: $$$\frac{x^{2}}{16} - \frac{x}{4} - \frac{11}{4} = 0$$$A.

Factored form: $$$\left(x - 2 + 4 \sqrt{3}\right) \left(x - 4 \sqrt{3} - 2\right) = 0$$$A.

Graph: see the graphing calculator.