## 2016年11月4日金曜日

### 数学 - 放物線・楕円・双曲線 - 2次曲線 – 放物線・楕円・双曲線(放物線)

1. $\begin{array}{l}\sqrt{{x}^{2}+{\left(y-2\right)}^{2}}=|y+2|\\ {x}^{2}+{y}^{2}-4y+4={y}^{2}+4y+4\\ y=\frac{1}{8}{x}^{2}\end{array}$

2. $\begin{array}{l}\sqrt{{x}^{2}+{\left(y+\frac{1}{8}\right)}^{2}}=|y-\frac{1}{8}|\\ {x}^{2}+{y}^{2}+\frac{1}{4}y+\frac{1}{64}={y}^{2}-\frac{1}{4}y+\frac{1}{64}\\ y=-2{x}^{2}\end{array}$

3. $\begin{array}{l}\sqrt{{\left(x-1\right)}^{2}+{y}^{2}}=|x+1|\\ {x}^{2}-2x+1+{y}^{2}={x}^{2}+2x+1\\ {y}^{2}=4\end{array}$

4. $\begin{array}{l}x=\frac{1}{2}\\ \sqrt{{\left(x+\frac{1}{2}\right)}^{2}+{y}^{2}}=|x-\frac{1}{2}|\\ {x}^{2}+x+\frac{1}{4}+{y}^{2}={x}^{2}-x+\frac{1}{4}\\ {y}^{2}=-2x\end{array}$

1. $\begin{array}{l}4·\frac{1}{4}y={x}^{2}\\ 焦点\left(0,\frac{1}{4}\right)準線y=-\frac{1}{4}\end{array}$

2. $\begin{array}{l}4·3y={x}^{2}\\ 焦点\left(0,3\right)準線y=-3\end{array}$

3. $\begin{array}{l}4·\left(-\frac{1}{2}\right)y={x}^{2}\\ 焦点\left(0,-\frac{1}{2}\right)準線y=\frac{1}{2}\end{array}$

4. $\begin{array}{l}4·1x={y}^{2}\\ 焦点\left(1,0\right)準線x=-1\end{array}$

5. $\begin{array}{l}4·\left(-\frac{1}{4}\right)x={y}^{2}\\ 焦点\left(-\frac{1}{4},0\right)準線y=\frac{1}{4}\end{array}$

6. $\begin{array}{l}{y}^{2}=4·2x\\ 焦点\left(2,0\right)準線y=-2\end{array}$