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Identify the conic section $$$\left(x + 196 y\right)^{2} = 49$$$
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Your Input
Identify and find the properties of the conic section $$$\left(x + 196 y\right)^{2} = 49$$$.
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, $$$A = 1$$$, $$$B = 392$$$, $$$C = 38416$$$, $$$D = 0$$$, $$$E = 0$$$, $$$F = -49$$$.
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
$$$\left(x + 196 y\right)^{2} = 49$$$A represents a pair of the lines $$$y = - \frac{1}{28}$$$, $$$y = \frac{1}{28}$$$A.
General form: $$$x^{2} + 392 x y + 38416 y^{2} - 49 = 0$$$A.
Factored form: $$$\left(28 y - 1\right) \left(28 y + 1\right) = 0$$$A.
Graph: see the graphing calculator.