Matrix Representation of Conic Sections

In mathematics, the matrix representation of conic sections is one way of studying a conic section, its axis, vertices, foci, tangents, and the relative position of a given point. We can also study conic sections whose axes aren't parallel to our coordinate system.

Conic sections have the form of a second-degree polynomial:

Q \ \stackrel{\mathrm{def}}{=}\ Ax^2+Bxy+Cy^2+Dx+Ey+F=0. \,

That can be written as:

\mathbf{x}^T A_Q\mathbf{x}=0

Where is the homogeneous coordinate vector:

\begin{pmatrix} x \\ y \\ 1 \end{pmatrix}

And a matrix:

A_Q = \begin{pmatrix} A & B/2 & D/2 \\ B/2 & C & E/2 \\ D/2 & E/2 & F \end{pmatrix}.

Read more about Matrix Representation Of Conic Sections:  Classification, Center, Axes, Vertices, Tangents, Reduced Equation

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