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Step 1 A nondegenerate conic section of the form, Ax2+By2+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 B and AB>0
4) A hyperbola if AB<0
Step 2 Given that, 3x2+2y2+12x−4y+2=0 Here A=3 and B=2 So A and B are not equal and AB=(3)(2)=6>0 Hence the graph of the equation is ellipse.
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