Identify the conic section $\frac{x^{2}}{3} = 4$

Identify and find the properties of the conic section $\frac{x^{2}}{3} = 4$.

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, $A = \frac{1}{3}$, $B = 0$, $C = 0$, $D = 0$, $E = 0$, $F = -4$.

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.

$\frac{x^{2}}{3} = 4$A represents a pair of the lines $x = - 2 \sqrt{3}$, $x = 2 \sqrt{3}$A.

General form: $\frac{x^{2}}{3} - 4 = 0$A.

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

Graph: see the graphing calculator.