I have the general equationAx2+Bxy+Cy2+Dx+Ey+F=0and I want to determine what conic section it represents according to the value of its coefficients or relations between them, is there a theorem where that is explained?

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Laylah Hebert · Accepted Answer

This equation can be written in matrix notation, in terms of a symmetric matrix to simplify some subsequent formulae, asQ=(x,y)(AB/2B/2C)(x,y)T+(D&amp;nbsp;E)(x,y)T+F=0.the first matrix X is called the matrix of the quadratic form.Q is a hyperbola if and only if det&amp;nbsp;A&amp;lt;0,Q is a parabola if and only if det&amp;nbsp;A=0, andQ is an ellipse if and only if det&amp;nbsp;A&amp;gt;0.

I have the general equation \(\displaystyle{A}{x}^{{2}}+{B}{x}{y}+{C}{y}^{{2}}+{D}{x}+{E}{y}+{F}={0}\) and I want

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