优优班--学霸训练营 > 知识点挑题
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            • 1.
              已知直线\(l\)经过两条直线\(2x-y-3=0\)和\(4x-3y-5=0\)的交点,且与直线\(x+y-2=0\)垂直.
              \((1)\)求直线\(l\)的方程;
              \((2)\)若圆\(C\)的圆心为点\((3,0)\),直线\(l\)被该圆所截得的弦长为\(2 \sqrt {2}\),求圆\(C\)的标准方程.
            • 2.
              圆心在直线\(x-2y=0\)上的圆\(C\)与\(y\)轴的正半轴相切,圆\(C\)截\(x\)轴所得弦的长为\(2 \sqrt {3}\),则圆\(C\)的标准方程为 ______ .
            • 3.

              已知圆\(C\)的圆心在\(x\)轴的正半轴上,点\(M(0,\sqrt{5})\)在圆\(C\)上,且圆心到直线\(2x-y=0\)的距离为\(\dfrac{4\sqrt{5}}{5}\),那么圆\(C\)的方程为________.

            • 4.

              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.\(4\sqrt{2} \)
            • 5.

              一束光线从点\(A\left( -1,1 \right)\)出发,经\(x\)轴反射到圆\(C:{{\left( x-2 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=1\)上的最短路程是(    )

              A.\(3\sqrt{2}-1\)
              B.\(2\sqrt{6}\)
              C.\(4\)
              D.\(5\)
            • 6.

              已知圆心为\(C\)的圆经过点\(A(0,-6)\),\(B(1,-5)\),且圆心在直线\(l\):\(x-y+1=0\)上,则圆的标准方程为________.

            • 7.

              下面给出四个命题的表述:

              \(①\)直线\((3+m)x+4y-3+3m=0(m∈R)\)恒过定点\((-3,3)\);

              \(②\)线段\(AB\)的端点\(B\)的坐标是\((3,4)\),\(A\)在圆\(x^{2}+y^{2}=4\)上运动,则线段\(AB\)的中点\(M\)的轨迹方程\({{\left( x-\dfrac{3}{2} \right)}^{2}}+{{(y-2)}^{2}}=1\);

              \(③\)已知\(M=\left\{ \left.\left(x,y\right) \right|y= \sqrt{1-{x}^{2}}\right\} \),\(N=\{(x,y)|y=x+b\}\),若\(M∩N\neq \varnothing \),则\(b∈\left[- \sqrt{2}, \sqrt{2}\right] \);

              \(④\)已知圆\(C:(x-b)^{2}+(y-c)^{2}=a^{2}(a > 0,b > 0,c > 0)\)与\(x\)轴相交,与\(y\)轴相离,则直线\(ax+by+c=0\)与直线\(x+y+1=0\)的交点在第二象限.

              其中表述正确的是  \((\)    \()\)

              A.\(①②④\)
              B.\(①②③\)
              C.\(①③\)
              D.\(①②③④\)
            • 8.

              某学校有\(2500\)名学生,其中高一\(1000\)人,高二\(900\)人,高三\(600\)人,为了了解学生的身体健康状况,采用分层抽样的方法,若从本校学生中抽取\(100\)人,从高一和高三抽取样本数分别为\(a{,}b\),且直线\(ax{+}by{+}8{=}0\)与以\(A(1{,}{-}1)\)为圆心的圆交于\(B{,}C\)两点,且\({∠}BAC{=}120^{{∘}}\),则圆\(C\)的方程为______________

            • 9.

              已知函数\(f(x)=x+\sin x(x∈R)\),且\(f(y-2y+3)+f(x^{2}-4x+1)\leqslant 0\),则当\(y\geqslant 1\)时,\( \dfrac{y}{x+1}\)的取值范围是\((\)  \()\)

              A.\(\left[ \left. \dfrac{1}{4}, \dfrac{3}{4} \right. \right]\)
              B.\(\left[ \left. \dfrac{1}{4},1 \right. \right]\)

              C.\([1,3 \sqrt{2}-3]\)                       
              D.\(\left[ \left. \dfrac{1}{3},+∞ \right. \right) \)
            • 10.
              已知圆\(C\)的圆心\(C\)在直线\(y=x-1\),且圆\(C\)经过曲线\(y=-x^{2}+6x-8\)与\(x\)轴的交点.
              \((1)\)求圆\(C\)的方程;
              \((2)\)已知过坐标原点\(O\)的直线\(l\)与圆\(C\)交\(M\),\(N\)两点,若\( \overrightarrow{ON}=2 \overrightarrow{OM}\),求直线\(l\)的方程.
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