= Degenerate conic
{title2=$\det Q=0$}
{wiki}
For $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$, the homogeneous quadratic coefficient matrix is
$$
Q=\begin{pmatrix}A&B/2&D/2\\B/2&C&E/2\\D/2&E/2&F\end{pmatrix}.
$$
The conic is degenerate when $Q$ is a <singular matrix>. Examples over the <real numbers> include the point $x^2+y^2=0$, the repeated line $y^2=0$, and the two <straight lines> in $xy=0$. The real solution set alone need not reveal the algebraic distinction: $x^2+y^2=-1$ has no real points, but its matrix is nonsingular. This determinant test is different from the <conic type discriminant>, which only uses the quadratic part in $x,y$.
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