How do you classify the conic $3x^2+y^2+2x+2y=0$ ?

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Answer 1 · 2017-01-20T08:18:32

$3x^2+y^2+2x+2y=0$ is an ellipse.

Let the equation be of the type $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$

then if

$B^2-4AC=0$ and $A=0$ or $C=0$ , it is a parabola

$B^2-4AC<0$ and $A=C$ , it is a circle

$B^2-4AC<0$ and $A!=C$ , it is an ellipse

$B^2-4AC>0$ , it is a hyperbola

In the given equation $3x^2+y^2+2x+2y=0$

$A=3$ , $B=0$ and $C=1$

Therefore, $B^2-4AC=0^2-4xx3xx1=-12<0$ and $A!=C$

Hence, $3x^2+y^2+2x+2y=0$ is an ellipse.
graph{3x^2+y^2+2x+2y=0 [-2.55, 2.45, -2.2, 0.3]}

How do you classify the conic 3x^2+y^2+2x+2y=03x^2+y^2+2x+2y=0?