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Identify the conic section $$$7 x^{2} - 14 x - 66 = -10$$$
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Your Input
Identify and find the properties of the conic section $$$7 x^{2} - 14 x - 66 = -10$$$.
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, $$$A = 7$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = -14$$$, $$$E = 0$$$, $$$F = -56$$$.
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.
Answer
$$$7 x^{2} - 14 x - 66 = -10$$$A represents a pair of the lines $$$x = -2$$$, $$$x = 4$$$A.
General form: $$$7 x^{2} - 14 x - 56 = 0$$$A.
Factored form: $$$\left(x - 4\right) \left(x + 2\right) = 0$$$A.
Graph: see the graphing calculator.