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(A) The general equation of a second-degree curve is given by $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$.Comparing the given equation $8 x^2+12 y^2-4 x+4 y

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an ellipse

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(A) The general equation of a second-degree curve is given by $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$.Comparing the given equation $8 x^2+12 y^2-4 x+4 y-1=0$ with the general form,we have $a=8$,$b=12$,and $h=0$.The nature of the conic section is determined by the discriminant $h^2-a b$.Here,$h^2-a b = (0)^2 - (8)(12) = -96$.Since $h^2-a b < 0$ and $a 
eq b$,the equation represents an ellipse.

The equation $8 x^2+12 y^2-4 x+4 y-1=0$ represents

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