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Identify the conic section $$$\left(- 2 x - 6\right)^{2} = 0$$$
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Your Input
Identify and find the properties of the conic section $$$\left(- 2 x - 6\right)^{2} = 0$$$.
Solution
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, $$$A = 4$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = 24$$$, $$$E = 0$$$, $$$F = 36$$$.
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 a line.
Answer
$$$\left(- 2 x - 6\right)^{2} = 0$$$A represents the line $$$x = -3$$$A.
General form: $$$4 x^{2} + 24 x + 36 = 0$$$A.
Factored form: $$$\left(x + 3\right)^{2} = 0$$$A.
Graph: see the graphing calculator.