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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>
The square of the [[Euclidean norm]] in ''n''-dimensional space, the most commonly used measure of distance, is
:<math>x_1^2+\cdots+x_n^2.</math>
In two dimensions this means that the distance between two points is the square root of the sum of the squared distances along the <math>x_1</math> axis and the <math>x_2</math> axis.
==Matrix form==
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