# 二次曲面

Ellipse (e = 1/2), parabola (e = 1) and hyperbola (e = 2) with fixed focus F and directrix.

${\displaystyle \sum _{i,j=0}^{D}Q_{i,j}x_{i}x_{j}+\sum _{i=0}^{D}P_{i}x_{i}+R=0}$

${\displaystyle \mathbf {x} ={\begin{pmatrix}x_{1}\\x_{2}\\\vdots \\x_{n}\\\end{pmatrix}};}$　${\displaystyle A={\begin{pmatrix}a_{11}&a_{12}&\cdots &a_{1n}\\a_{12}&a_{22}&\cdots &a_{2n}\\\vdots &\vdots &\ddots &\vdots \\a_{1n}&a_{2n}&\cdots &a_{nn}\\\end{pmatrix}};}$　${\displaystyle \mathbf {b} ={\begin{pmatrix}b_{1}\\b_{2}\\\vdots \\b_{n}\end{pmatrix}}}$
${\displaystyle \langle A\mathbf {x} ,\mathbf {x} \rangle +\langle \mathbf {b} ,\mathbf {x} \rangle +c=0}$

## 参考来源

1. ^ [1], Quadrics in Geometry Formulas and Facts by Silvio Levy, excerpted from 30th Edition of the CRC Standard Mathematical Tables and Formulas (CRC Press).