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

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

2021-02-26
Step 1 A nondegenerate conic section of the form, $$Ax^2 + By^2 + Cx + Dy + E=0$$ 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 $$B and AB > 0$$ 4) A hyperbola if $$AB < 0$$ Step 2 Given that, $$3x^2 + 2y^2 + 12x − 4y + 2 = 0$$ 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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