优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知圆\(C\)经过点\(P(-2,4)\)和点\(Q(4,4)\),直径为\(2 \sqrt{10}\),则圆\(C\)的标准方程为\((\)  \()\)


              A.\((x-1)^{2}+(y-3)^{2}=10\)

              B.\((x+1)^{2}+(y-5)^{2}=10\)

              C.\((x+1)^{2}+(y-3)^{2}=10\)或\((x-1)^{2}+(y-5)^{2}=10\)

              D.\((x-1)^{2}+(y-3)^{2}=10\)或\((x-1)^{2}+(y-5)^{2}=10\)
            • 2.
              以\((1,-1)\)为圆心且与直线\(x+y- \sqrt {6}=0\)相切的圆的方程为\((\)  \()\)
              A.\((x+1)^{2}+(y-1)^{2}=6\)
              B.\((x-1)^{2}+(y+1)^{2}=6\)
              C.\((x+1)^{2}+(y-1)^{2}=3\)
              D.\((x-1)^{2}+(y+1)^{2}=3\)
            • 3. 已知圆\(C\)过两点\(M(-3,3)\),\(N(1,-5)\),且圆心\(C\)在直线\(2x-y-2=0\)上.
              \((\)Ⅰ\()\)求圆\(C\)的标准方程;
              \((\)Ⅱ\()\)直线\(l\)过点\((-2,5)\)且与圆\(C\)有两个不同的交点\(A\),\(B\),若直线\(l\)的斜率\(k\)大于\(0\),求\(k\)的取值范围;

            • 4. 已知圆的圆心为\((1,2)\)和圆上的一点为\((-2,6)\),求圆的标准方程.
            • 5.
              已知平面直角坐标系\(xOy{中},A(4+2 \sqrt {3},2),B(4,4)\),圆\(C\)是\(\triangle OAB\)的外接圆.
              \((1)\)求圆\(C\)的方程;
              \((2)\)若过点\((2,6)\)的直线\(l\)被圆\(C\)所截得的弦长为\(4 \sqrt {3}\),求直线\(l\)的方程.
            • 6.

              已知\(θ∈R\),则方程\({{x}^{2}}+\dfrac{{{y}^{2}}}{\cos \theta }=4\)表示的曲线不可能是\((\)    \()\)

              A.圆
              B.椭圆
              C.双曲线
              D.抛物线
            • 7.

              半径长为\(6\)的圆与\(x\)轴相切,且与圆\(x^{2}+(y-3)^{2}=1\)内切,则此圆的方程为\((\)  \()\)

              A.\((x-4)^{2}+(y-6)^{2}=6\)

              B.\((x±4)^{2}+(y-6)^{2}=6\)

              C.\((x-4)^{2}+(y-6)^{2}=36\)

              D.\((x±4)^{2}+(y-6)^{2}=36\)
            • 8.

              求以\(A(2,2)\),\(B(5,3)\),\(C(3,-1)\)为顶点的三角形的外接圆的方程.

            • 9. 圆心为\((1,1)\)且过原点的圆的方程是 ______ .
            • 10.

              设两圆\(C_{1}\),\(C_{2}\)都和两坐标轴相切,且都过点\((4,1)\),则两圆心的距离\(|C_{1}C_{2}|\)等于\((\)  \()\)

              A.\(4\)                                              
              B.\(4 \sqrt{2}\)

              C.\(8\)                                              
              D.\(8 \sqrt{2}\)
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