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This quadratic form is positive definite if <math>c_1>0</math> and <math>c_1c_2-{c_3}^2>0,</math> negative definite if <math>c_1<0</math> and <math>c_1c_2-{c_3}^2>0,</math> and indefinite if <math>c_1c_2-{c_3}^2<0.</math> It is positive or negative semidefinite if <math>c_1c_2-{c_3}^2=0,</math> with the sign of the semidefiniteness coinciding with the sign of <math>c_1.</math>
This bivariate quadratic form appears in the context of [[conic section]]s centered on the origin. If the general quadratic form above is equated to 0, the resulting equation is that of an [[ellipse]] if the quadratic form is positive or negative definite, a [[hyperbola]] if it is indefinite, and a [[parabola]] if <math>c_1c_2-{c_3}^2=0.</math>
==Matrix form==
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