知识点1直线的参数方程
$\left\{\begin{array}{l}x=x_{0}+t \cos \alpha \\ y=y_{0}+\operatorname{tsin} \alpha\end{array}\right.$($t为参数，α为直线倾斜角$)
知识点2椭圆的参数方程
$\left\{\begin{array}{l}x=a \cos \varphi \\ y=b \sin \varphi\end{array}\right.$($φ为参数$)
知识点3双曲线的参数方程
双曲线的参数方程:$\left\{\begin{array}{l}x=asecφ \\ y=btanφ\end{array}\right.$($φ为参数$)
$secφ与cosφ$互为倒数关系.
知识点4圆的参数方程
$\left\{\begin{array}{l}x=a+rcosφ \\ y=b +rsinφ\end{array}\right.$($φ为参数$)
知识点5抛物线的参数方程
1.焦点在$x$正半轴
$\left\{\begin{array}{l}x=2pt^{2} \\y=2pt\end{array}\right.$($t为参数$)
2.焦点在$y$正半轴
$\left\{\begin{array}{l}y=2pt^{2} \\x=2pt\end{array}\right.$($t为参数$)
直线参数方程$t$的几何意义
1.过点$P_{0}$($x_{0},y_{0}$)，倾斜角为$α$的直线$l$的参数方程是：$\left\{\begin{array}{l}x=x_{0}+t \cos \alpha \\ y=y_{0}+\operatorname{tsin}\alpha\end{array}\right.$($t为参数$)$t$的几何意义：|$t$|表示直线上动点$P$($x,y$)到定点$P_{0}$的距离，即|$t$|=$|\overrightarrow{P_{0} P}|$.
所以在定点$P_{0}$异侧的动点对应的参数正负相反.
2.若$P_{1}、P_{2}$是直线上两点，所对应的参数分别为$t_{1}、t_{2}$，$∣P_{1}P_{2}=∣t_{2}－t_{1}∣$，常用于直线与圆锥曲线相交时求弦长.
3.若$P_{1}、P_{2}、P_{3}$是直线上的点，所对应的参数分别为$t_{1}、t_{2}、t_{3}$，则$P_{1}P_{2}$中点$P_{3}$的参数为$t_{3}$＝$\frac{t_{1}+t_{2}}{2}$，∣$P_{0}P_{3}$∣=$|\frac{t_{1}+t_{2}}{2}|$
4.若定点$P_{0}$为$P_{1}、P_{2}$的中点，则$t_{1}+t_{2}=0$，$t_{1}·t_{2}<0$.