Identify the conic section $$$\left(y - 1\right)^{2} - 64 = 0$$$

Identify and find the properties of the conic section $$$\left(y - 1\right)^{2} - 64 = 0$$$.

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, $$$A = 0$$$, $$$B = 0$$$, $$$C = 1$$$, $$$D = 0$$$, $$$E = -2$$$, $$$F = -63$$$.

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.

$$$\left(y - 1\right)^{2} - 64 = 0$$$A represents a pair of the lines $$$y = -7$$$, $$$y = 9$$$A.

General form: $$$y^{2} - 2 y - 63 = 0$$$A.

Factored form: $$$\left(y - 9\right) \left(y + 7\right) = 0$$$A.

Graph: see the graphing calculator.