Identify the conic section $$$6554 - y^{2} = 0$$$

Identify and find the properties of the conic section $$$6554 - y^{2} = 0$$$.

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, $$$A = 0$$$, $$$B = 0$$$, $$$C = 1$$$, $$$D = 0$$$, $$$E = 0$$$, $$$F = -6554$$$.

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.

$$$6554 - y^{2} = 0$$$A represents a pair of the lines $$$y = - \sqrt{6554}$$$, $$$y = \sqrt{6554}$$$A.

General form: $$$y^{2} - 6554 = 0$$$A.

Factored form: $$$\left(y - \sqrt{6554}\right) \left(y + \sqrt{6554}\right) = 0$$$A.

Graph: see the graphing calculator.