过五点作椭圆或圆并给出各种坐标,参数,方程

hbghlyj

见cjhb.site/30
输出示例:

$\begin{array}{cc}
\text{Equation} & 5 x^2+6 x y+22 x+5 y^2-26 y+29=0 \\
\text{Foci} & \left(
\begin{array}{cc}
\frac{1}{8} \left(-\sqrt{1383}-47\right) & \frac{1}{8} \left(\sqrt{1383}+49\right) \\
\frac{1}{8} \left(\sqrt{1383}-47\right) & \frac{1}{8} \left(49-\sqrt{1383}\right) \\
\end{array}
\right) \\
\text{Vertices} & \left(
\begin{array}{cc}
\frac{1}{8} \left(-2 \sqrt{461}-47\right) & \frac{1}{8} \left(2 \sqrt{461}+49\right) \\
\frac{1}{8} \left(2 \sqrt{461}-47\right) & \frac{1}{8} \left(49-2 \sqrt{461}\right) \\
\end{array}
\right) \\
\text{Covertices} & \left(
\begin{array}{cc}
\frac{1}{8} \left(\sqrt{461}-47\right) & \frac{1}{8} \left(\sqrt{461}+49\right) \\
\frac{1}{8} \left(-\sqrt{461}-47\right) & \frac{1}{8} \left(49-\sqrt{461}\right) \\
\end{array}
\right) \\
\text{Center} & \left\{-\frac{47}{8},\frac{49}{8}\right\} \\
\text{Semimajor Axis Length} & \frac{\sqrt{\frac{461}{2}}}{2} \\
\text{Semiminor Axis Length} & \frac{\sqrt{\frac{461}{2}}}{4} \\
\text{Linear Eccentricity} & \frac{\sqrt{\frac{1383}{2}}}{4} \\
\text{Major Axis} & 4 (x+y)=1 \\
\text{Minor Axis} & x+12=y \\
\text{Area} & \frac{461 \pi }{16} \\
\text{Circumference} & 36.7731 \\
\text{Semilatus Rectum} & \frac{\sqrt{\frac{461}{2}}}{8} \\
\text{Focal Parameter} & \frac{\sqrt{\frac{461}{6}}}{4} \\
\text{Eccentricity} & \frac{\sqrt{3}}{2} \\
\text{Apoapsis} & \frac{1}{4} \sqrt{\frac{461}{2}} \left(\sqrt{3}+2\right) \\
\text{Periapsis} & -\frac{1}{4} \sqrt{\frac{461}{2}} \left(\sqrt{3}-2\right) \\
\text{Range of y} & \left\{\frac{1}{8} \left(49-\sqrt{2305}\right),\frac{1}{8} \left(\sqrt{2305}+49\right)\right\} \\
\text{Range of x} & \left\{\frac{1}{8} \left(-\sqrt{2305}-47\right),\frac{1}{8} \left(\sqrt{2305}-47\right)\right\} \\
\end{array}$
从上到下依次为:
方程,焦点坐标,长轴端点坐标,短轴端点坐标,中心坐标,半长轴长,半短轴长,半焦距,长轴方程,短轴方程,面积,周长,半通径(半正焦弦长),焦准距,离心率,最长焦半径,最短焦半径,y的范围,x的范围