设弦端点$A(x_{1},y_{1})，B(x_{2},y_{2})$，由直线联立曲线方程消去$y$得到关于x的一元二次方程$ax^{2}+bx+c = 0$，$△>0$，$α$为直线$AB$的倾斜角，$k$为直线的斜率，则:
1.$|AB|$ = $\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$
2.$|AB|$=$\sqrt{\left(1+k^{2}\right)}|x_{1}-x_{2}|$
$=\sqrt{\left(1+\frac{1}{k^{2}}\right)}|y_{1}-y_{2}|$
$=\sqrt{\left(1+k^{2}\right)}\sqrt{(x_{1}+x_{2})^{2}-4x_{1}x_{2}}$
$=\sqrt{\left(1+\frac{1}{k^{2}}\right)}\sqrt{(y_{1}+y_{2})^{2}-4y_{1}y_{2}}$ .
3.$|AB|$ = $\sqrt{\left(1+k^{2}\right)\left(x_{2}-x_{1}\right)^{2}}$=$\left|x_{1}-x_{2}\right| \sqrt{1+\tan ^{2} \alpha}$=$\left|y_{1}-y_{2}\right| \sqrt{1+\cot ^{2} \alpha}$.