优优班--学霸训练营 > 知识点挑题
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            • 1.

              过点\(P(-1,3)\)且平行于直线\(x-2y+3=0\)的直线方程为(    )

              A.\(2x+y-1=0\) 
              B.\(2x+y-5=0\)
              C.\(x-2y+7=0\) 
              D.\(x-2y+5=0\)
            • 2.

              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.\(①②③④\)
            • 3.

              和直线\(3x-4y+5=0\)关于\(x\)轴对称的直线方程为(    )

              A.\(3x+4y+5=0\) 

              B.\(3x+4y-5=0\)

              C.\(-3x+4y-5=0\) 

              D.\(-3x+4y+5=0\)
            • 4.

              过点\((1,0)\)且与直线\(x-2y-2=0\)平行的直线方程是\((\)  \()\)

              A.\(x-2y-1=0\)               
              B.\(x-2y+1=0\)       
              C.\(2x+y-2=0\)                 
              D.\(x+2y-1=0\)
            • 5.

              过点\((1,2)\)的直线\(l\)与两坐标轴的正半轴分别交于\(A\)、\(B\)两点,\(O\)为坐标原点,当\(\triangle OAB\)面积最小时,直线\(l\)的方程为(    )

              A.\(2x+y-4=0\)                              
              B.\(x+2y-5=0\)

              C.\(x+y-3=0\)                                
              D.\(2x+3y-8=0\)
            • 6.

              数学家欧拉在\(1765\)年提出定理:三角形的外心、重心、垂心依次位于同一直线上,且重心到外心的距离是重心到垂心距离的一半,这条直线被后人称之为三角形的欧拉线\(.\)已知\(\Delta ABC\)的顶点\(A(2,0),B(0,4)\),\(AC=BC\),则\(\Delta ABC\)的欧拉线方程为\((\)    \()\)

              A.\(x-2y+3=0\)
              B.\(x+2y+3=0\)
              C.\(2x+y+3=0\)
              D.\(2x-y+3=0\)
            • 7.

              若动点\(A\left({x}_{1},{y}_{1}\right)B\left({x}_{2},{y}_{2}\right) \)分别在直线\(l_{1}\):\(x+y-11=0\)和\(l_{2}\):\(x+y-1=0\)上移动,则\(AB\)中点\(M\)所在直线方程为 \((\)   \()\)

              A.\(x+y-6=0\)   
              B.\(x-y-6=0\)   
              C.\(x+y+6=0\)   
              D.\(x-y+6=0\)
            • 8.
              经过点\(A(1,2)\)并且在两个坐标轴上的截距的绝对值相等的直线方程为\((\)  \()\)
              A.\(y=2x\)或\(x-y+1=0\)
              B.\(y=2x\),\(x+y-3=0\)
              C.\(x+y-3=0\),或\(x-y+1=0\)
              D.\(y=2x\),或\(x+y-3=0\),或\(x-y+1=0\)
            • 9.

              经过抛物线\(y^{2}=2x\)的焦点且平行于直线\(3x-2y+5=0\)的直线\(l\)的方程是\((\)   \()\)

              A.\(6x-4y-3=0\)
              B.\(3x-2y-3=0\)
              C.\(2x+3y-2=0\)
              D.\(2x+3y-1=0\)
            • 10.

              若动点\(A(x_{1},y_{1})\)、\(B(x_{2},y_{2})\)分别在直线\(l_{2}\):\(x+y-11=0\)和\(l_{2}\):\(x+y-1=0\)上移动,则\(AB\)中点\(M\)所在直线方程为\((\)   \()\)

              A.\(x-y-6=0\)
              B.\(x+y+6=0\)
              C.\(x-y+6=0\)
              D.\(x+y-6=0\)
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