Identify the conic section $$$\left(x - 4\right)^{2} + \left(y + 5\right)^{2} = 4$$$
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Identify and find the properties of the conic section $$$\left(x - 4\right)^{2} + \left(y + 5\right)^{2} = 4$$$.
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, $$$A = 1$$$, $$$B = 0$$$, $$$C = 1$$$, $$$D = -8$$$, $$$E = 10$$$, $$$F = 37$$$.
The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = -16$$$.
Next, $$$B^{2} - 4 A C = -4$$$.
Since $$$B^{2} - 4 A C \lt 0$$$, the equation represents a circle.
To find its properties, use the circle calculator.
Answer
$$$\left(x - 4\right)^{2} + \left(y + 5\right)^{2} = 4$$$A represents a circle.
General form: $$$x^{2} - 8 x + y^{2} + 10 y + 37 = 0$$$A.
Graph: see the graphing calculator.