Question

7．可以将椭圆$\frac{{x}^{2}}{10}$+$\frac{{y}^{2}}{8}$=1变为圆x²+y²=4的伸缩变换为（　　）

• A． $\left\{\begin{array}{l}{\sqrt{2}x′=\sqrt{5}x}\\{y′=\sqrt{2}y}\end{array}\right.$
• B． $\left\{\begin{array}{l}{\sqrt{2}x′=x}\\{\sqrt{5}y′=\sqrt{2}y}\end{array}\right.$
• C． $\left\{\begin{array}{l}{\sqrt{5}x′=\sqrt{2}x}\\{\sqrt{2}y′=y}\end{array}\right.$
• D． $\left\{\begin{array}{l}{5x′=2x}\\{\sqrt{2}y′=y}\end{array}\right.$

Answer 1

分析 利用椭圆化为圆的伸缩变换公式即可得出．

解答 解：椭圆$\frac{{x}^{2}}{10}$+$\frac{{y}^{2}}{8}$=1化为$\frac{2{x}^{2}}{5}+\frac{{y}^{2}}{2}$=4，
令$\left\{\begin{array}{l}{\sqrt{5}{x}^{′}=\sqrt{2}x}\\{\sqrt{2}{y}^{′}=y}\end{array}\right.$即可化为（x′）²+（y′）²=4，
故选：C．

点评 本题考查了椭圆化为圆的伸缩变换公式，属于基础题．