共50条信息
将曲线\(C\)按伸缩变换公式\(\begin{cases}x{{{"}}}=2x \\ y{{{"}}}=3y\end{cases} \)变换后的曲线方程为\((x{{"}})^{2}+(y{{"}})^{2}=1\),则曲线\(C\)的方程为 \((\) \()\)
在同一坐标系中,将曲线\(y=2\sin 3x\)变为曲线\(y=\sin x\)的伸缩变换是( )
将椭圆\(\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{4}=1\)按\(φ:\begin{cases} & x{{{"}}}=\lambda { }x(\lambda > 0) \\ & y{{{"}}}=\mu { }y{(}\mu > {0)} \end{cases}\) ,变换后得到圆\(x{{{{{"}}}}^{2}}+y{{{{{"}}}}^{2}}=9\),则\((\) \()\)
已知曲线\(C\)的极坐标方程为\(\rho^{2}{=}\dfrac{12}{3\cos^{2}\theta{+}4\sin^{2}\theta}\),以极点为原点,极轴为\(x\)轴非负半轴建立平面直角坐标系,则曲线\(C\)经过伸缩变换\(\begin{cases}{x}^{,}= \dfrac{1}{2}x \\ {y}^{,}= \dfrac{ \sqrt{3}}{3}y\end{cases} \)后,得到的曲线是\((\) \()\)
将曲线\(C\)按伸缩变换公式\({ }\!\!\{\!\!{ }\begin{matrix} {x}{{{"}}}=2x \\ {y}{{{"}}}=3y \\\end{matrix}{ }\)变换后的曲线方程为\({{\left( {{x}{{{"}}}} \right)}^{2}}+{{\left( {{y}{{{"}}}} \right)}^{2}}=1\),则曲线\(C\)的方程为 \((\) \()\)
欲将方程\(\dfrac{{{x}^{2}}}{4}+\dfrac{{{y}^{2}}}{3}=1\)所对应的图形变成方程\({{x}^{2}}+{{y}^{2}}=1\)所对应的图形,需经过伸缩变换\(\varphi \)为\((\) \()\)
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