## 2016年11月27日日曜日

### 数学 - 2次曲線と直線 - 2次曲線 – 2次曲線と直線(2次曲線の平行移動)

1. $\begin{array}{l}y\left(y+1\right)=x\\ 放物線\end{array}$

2. $\begin{array}{l}x=\frac{1}{2}{y}^{2}+2\\ 放物線\end{array}$

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

4. $双曲線$

5. $\begin{array}{l}4{\left(x-3\right)}^{2}-36+9{y}^{2}=0\\ \frac{{\left(x-3\right)}^{2}}{9}+\frac{{y}^{2}}{4}=1\\ 楕円\end{array}$

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

7. $\begin{array}{l}{x}^{2}-{\left(y-2\right)}^{2}+4-5=0\\ {x}^{2}-{\left(y-2\right)}^{2}=1\\ 双曲線\end{array}$

8. $\begin{array}{l}2{\left(x-1\right)}^{2}-2-{\left(y+2\right)}^{2}+4=0\\ {\left(x-2\right)}^{2}-\frac{{\left(y+2\right)}^{2}}{2}=-1\\ 双曲線\end{array}$

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