优优班--学霸训练营 > 知识点挑题
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            • 1.
              在直角坐标系\(xOy\)中,点\(A(-2,2).\)以坐标原点为极点,\(x\)轴正半轴为极轴建立极坐标系,点\(A\)的极坐标为\((\)  \()\)
              A.\((2 \sqrt {2}, \dfrac {π}{4})\)
              B.\((2 \sqrt {2}, \dfrac {3π}{4})\)
              C.\(( \sqrt {2}, \dfrac {π}{4})\)
              D.\(( \sqrt {2}, \dfrac {3π}{4})\)
            • 2.
              参数方程\( \begin{cases} \overset{x=3t^{2}+4}{y=t^{2}-2}\end{cases}(t\)为参数,且\(0\leqslant t\leqslant 3)\)所表示的曲线是\((\)  \()\)
              A.直线
              B.圆弧
              C.线段
              D.双曲线的一支
            • 3.
              在极坐标系中,圆\(ρ=\cos (θ+ \dfrac {π}{3})\)的圆心的极坐标为\((\)  \()\)
              A.\(( \dfrac {1}{2},- \dfrac {π}{3})\)
              B.\(( \dfrac {1}{2}, \dfrac {π}{3})\)
              C.\((1,- \dfrac {π}{3})\)
              D.\((1, \dfrac {π}{3})\)
            • 4.

              极坐标方程\(θ= \dfrac{π}{3}\left(ρ > 0\right),θ= \dfrac{2π}{3}\left(ρ > 0\right) \)和\(\rho =4\)所表示的曲线围成的面积为\((\)   \()\)

              A.\(\dfrac{16\pi }{3}\)
              B.\(\dfrac{8\pi }{3}\)
              C.\(\dfrac{4\pi }{3}\)
              D.\(\dfrac{2\pi }{3}\)
            • 5. 在极坐标系中,点\(A\)的极坐标是\((1,π)\),点\(P\)是曲线\(C\):\(ρ=2\sin θ\)上的动点,则\(|PA|\)的最小值是(    )
              A.\(0\)        
              B.\( \sqrt{2}\)
              C.\( \sqrt{2}\)\(+1\)            
              D.\( \sqrt{2}\)\(-1\)
            • 6.

              已知点\(M\)的极坐标是\(({-}2{,-}\dfrac{\pi}{6})\),它关于直线\(\theta{=}\dfrac{\pi}{2}\)的对称点坐标是\(({  })\)

              A.\((2{,}\dfrac{11\pi}{6})\)
              B.\(({-}2{,}\dfrac{7\pi}{6})\)
              C.\((2{,-}\dfrac{\pi}{6})\)
              D.\(({-}2{,-}\dfrac{11\pi}{6})\)
            • 7. 在极坐标系中,点\(\left( \left. 2, \dfrac{π}{3} \right. \right)\)到圆\(ρ=2\cos θ\)的圆心的距离为\((\)  \()\)
              A.\(2\)    
              B.\( \sqrt{4+ \dfrac{π^{2}}{9}}\)
              C.\( \sqrt{1+ \dfrac{π^{2}}{9}}\)
              D.\( \sqrt{3}\)
            • 8.

              已知点\(M\)的极坐标是\((2{,}{-}\dfrac{\pi}{6})\),它关于直线\(\theta{=}\dfrac{\pi}{2}\)的对称点坐标是\(({  })\)

              A.\((2{,}\dfrac{11\pi}{6})\)
              B.\((2{,}\dfrac{7\pi}{6})\)
              C.\((2{,}{-}\dfrac{\pi}{6})\)
              D.\((2{,}{-}\dfrac{11\pi}{6})\)
            • 9.

              曲线\(C_{1}\)的参数方程为\(\begin{cases}x= \sqrt{2}\cos α \\ y=1+ \sqrt{2}\sin α\end{cases} (α \)为参数\()\),以原点为极点,\(x\)轴的非负半轴为极轴建立极坐标系,曲线\(C_{2}\)的极坐标方程为\(\sqrt{2}p\sin (θ+ \dfrac{π}{4})=5 .\)设点\(P\),\(Q\)分别在曲线\(C\)\(1\)和\(C\)\(2\)上运动,则\(\left|PQ\right| \)的最小值为

              A.\(\sqrt{2} \)
              B.\(2\sqrt{2} \)
              C.\(3\sqrt{2} \)
              D.\(4\sqrt{2} \)
            • 10. 在极坐标系中,曲线\(ρ=4\sin (θ- \dfrac {π}{3})\)关于\((\)  \()\)
              A.直线\(θ= \dfrac {π}{3}\)轴对称
              B.直线\(θ= \dfrac {5}{6}π\)轴对称
              C.点\((2, \dfrac {π}{3})\)中心对称
              D.极点中心对称
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