# 空间曲线在 $xOy$ 平面上的投影曲线的方程（B011）

## 选项

[A].   $\left\{\begin{array}{l} F(x, y, z)=0 \\ G(x, y, z)=0 \end{array}\right.$ $\Rightarrow$ 消去 $y$ $\Rightarrow$ $\left\{\begin{array}{l} H(x, y)=0 \\ z=0 \end{array}\right.$

[B].   $\left\{\begin{array}{l} F(x, y, z)=0 \\ G(x, y, z)=0 \end{array}\right.$ $\Rightarrow$ 消去 $y$ $\Rightarrow$ $\left\{\begin{array}{l} H(x, z)=0 \\ z=0 \end{array}\right.$

[C].   $\left\{\begin{array}{l} F(x, y, z)=0 \\ G(x, y, z)=0 \end{array}\right.$ $\Rightarrow$ 消去 $z$ $\Rightarrow$ $\left\{\begin{array}{l} H(x, y)=0 \\ z=0 \end{array}\right.$

[D].   $\left\{\begin{array}{l} F(x, y, z)=0 \\ G(x, y, z)=0 \end{array}\right.$ $\Rightarrow$ 消去 $z$ $\Rightarrow$ $\left\{\begin{array}{l} H(x, y)=z \\ z=0 \end{array}\right.$

$\left\{\begin{array}{l} F(\textcolor{orange}{x}, \textcolor{orange}{y}, \textcolor{cyan}{z})=0 \\ G(\textcolor{orange}{x}, \textcolor{orange}{y}, \textcolor{cyan}{z})=0 \end{array}\right.$ $\Rightarrow$ 消去 $\textcolor{cyan}{z}$ $\Rightarrow$ $\left\{\begin{array}{l} H(\textcolor{orange}{x}, \textcolor{orange}{y})=0 \\ \textcolor{cyan}{z}=\textcolor{red}{0} \end{array}\right.$