# Identify the graph of the given nondegenerate conic sections: 3x^2 + 2y^2 + 12x - 4y + 2 = 0.

Identify the graph of the given nondegenerate conic sections: $3{x}^{2}+2{y}^{2}+12x-4y+2=0$.
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insonsipthinye

Step 1 A nondegenerate conic section of the form, $A{x}^{2}+B{y}^{2}+Cx+Dy+E=0$ Where A and B both are not zero.

1) A circle if $A=B$

2) A parabola if $AB=0$

3) An ellipse if A is not equal to

4) A hyperbola if $AB<0$

Step 2 Given that, $3{x}^{2}+2{y}^{2}+12x-4y+2=0$ Here So A and B are not equal and $AB=\left(3\right)\left(2\right)=6>0$ Hence the graph of the equation is ellipse.