优优班--学霸训练营 > 知识点挑题
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            • 1.

              曲线\(C\)的参数方程为\(\{\begin{matrix} x=4\cos \alpha \\ y=\sin \alpha \\\end{matrix}\) \((\alpha \)为参数\()\),\(M\)是曲线\(C\)上的动点,若曲线\(T\)极坐标方程\(2\rho {\sin }\theta +\rho {\cos }\theta =20\),则点\(M\)到\(T\)的距离的最大值为

              A.\(\sqrt{13}+4\sqrt{5}\)
              B.\(2+4\sqrt{5}\)
              C.\(4+4\sqrt{5}\)
              D.\(6\sqrt{5}\)
            • 2.
              与参数方程为\( \begin{cases} \overset{x= \sqrt {t}}{y=2 \sqrt {1-t}}\end{cases}(t\)为参数\()\)等价的普通方程为\((\)  \()\)
              A.\(x^{2}+ \dfrac {y^{2}}{4}=1\)
              B.\(x^{2}+ \dfrac {y^{2}}{4}=1(0\leqslant x\leqslant 1)\)
              C.\(x^{2}+ \dfrac {y^{2}}{4}=1(0\leqslant y\leqslant 2)\)
              D.\(x^{2}+ \dfrac {y^{2}}{4}=1(0\leqslant x\leqslant 1,0\leqslant y\leqslant 2)\)
            • 3. 在直角坐标系\(xOy\)中,直线\(l\)的参数方程为\( \begin{cases} \overset{x=t}{y=4+t}\end{cases}(t\)为参数\().\)以原点\(O\)为极点,以\(x\)轴的正半轴为极轴建立极坐标系,曲线\(C\)的极坐标方程为\(ρ=4 \sqrt {2}\sin (θ+ \dfrac {π}{4})\),则直 线\(l\)和曲线\(C\)的公共点有\((\)  \()\)
              A.\(0\)个
              B.\(1\)个
              C.\(2\)个
              D.无数个
            • 4.
              设曲线\(C\)的参数方程为 \((t\)为参数\()\),若以直角坐标系的原点为极点,\(x\)的正半轴为极轴建立极坐标系,则曲线\(C\)的极坐标方程是
              A.\(e\cos 2θ-\sin θ=0\)   
              B.\(e\cos θ= 0\)    
              C.    
              D.\(e=2\)
            • 5.
              已知直线\( \begin{cases} x=2+t \\ y=1+t\end{cases}(t\)为参数\()\)与曲线\(C\):\(ρ^{2}-4ρ\cos θ+3=0\)交于\(A\)、\(B\)两点,则\(|AB|=(\)  \()\)
              A.\(1\)
              B.\( \dfrac {1}{2}\)
              C.\( \dfrac { \sqrt {2}}{2}\)
              D.\( \sqrt {2}\)
            • 6.
              设直线\(l\)的参数方程为\( \begin{cases}x=a+t \\ y=b+t\end{cases}(t\)为参数\()\),\(l\)上的点\(P_{1}\)对应的参数为\(t_{1}\),则点\(P_{1}\)与点\(P(a,b)\)之间的距离是\((\)  \()\)
              A.\( \dfrac { \sqrt {2}}{2}|t_{1}|\)
              B.\(2|t_{1}|\)
              C.\( \sqrt {2}|t_{1}|\)
              D.\(|t_{1}|\)
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