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Identify the conic section $$$\left(y - 2\right)^{2} = - 8 x^{2}$$$
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Your Input
Identify and find the properties of the conic section $$$\left(y - 2\right)^{2} = - 8 x^{2}$$$.
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, $$$A = 8$$$, $$$B = 0$$$, $$$C = 1$$$, $$$D = 0$$$, $$$E = -4$$$, $$$F = 4$$$.
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, $$$B^{2} - 4 A C = -32$$$.
Since $$$\Delta = 0$$$, this is the degenerated conic section.
Since $$$B^{2} - 4 A C \lt 0$$$, the equation represents a single point.
Answer
$$$\left(y - 2\right)^{2} = - 8 x^{2}$$$A represents the point $$$\left(0, 2\right)$$$A.
General form: $$$8 x^{2} + y^{2} - 4 y + 4 = 0$$$A.