优优班--学霸训练营 > 知识点挑题
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            • 1.

              直线\(y=kx+3\)与圆\((x-3)^{2}+(y-2)^{2}=4\)相交于\(M\),\(N\)两点,若\(|MN|\geqslant 2\sqrt{3}\),则实数\(k\)的取值范围是\((\)    \()\)

              A.\(\left[ -\dfrac{3}{4},0 \right]\)
              B.\((−∞,− \dfrac{3}{4})∪[0,+∞) \)
              C.\(\left[ -\dfrac{\sqrt{3}}{3},\dfrac{\sqrt{3}}{3} \right]\)
              D.\(\left[ -\dfrac{2}{3},0 \right]\)
            • 2.

              直线\(\ell \):\(kx+y+4=0(k∈R)\)是圆\(C\):\(x^{2}+y^{2}+4x-4y+6=0\)的一条对称轴,过点\(A(0,k)\)作斜率为\(1\)的直线\(m\),则直线\(m\)被圆\(C\)所截得的弦长为\((\)  \()\)

              A.\(\dfrac{ \sqrt{2}}{2} \)
              B.\(\sqrt{2} \)
              C.\(\sqrt{6} \)
              D.\(2\sqrt{6} \)
            • 3.

              直线\(y=x\)被圆\((x−1)^{2}+y^{2}=1\)所截得的弦长为                  \((\)    \()\)

              A.\(\dfrac{\sqrt{2}}{2}\)
              B.\(1\)
              C.\(\sqrt{2}\)
              D.\(2\)
            • 4.

              直线\(y=x-1\)被圆\({{(x-3)}^{2}}+{{y}^{2}}=4\)截得的弦长为           

            • 5.

              已知圆\(C\)\(:\)\(x\)\({\,\!}^{2}\)\(+\)\((\)\(y-\)\(1)^{2}\)\(=\)\(5\),直线\(l\)\(:\)\(mx-y+\)\(1\)\(-m=\)\(0\)

              \((1)\)求证:对\(m\)\(∈R\),直线\(l\)与圆\(C\)总有两个不同的交点\(;\)

              \((2)\)设直线\(l\)与圆\(C\)交于\(A\)\(B\)两点,若\(|AB|=\)\( \sqrt{17} \),求直线\(l\)的倾斜角

            • 6.

              已知\(⊙C:{x}^{2}+{y}^{2}=1 \),直线\(l:x+y-1=0 \),则\(l\)被\(⊙C \)所截得的弦长为(    )

              A.\(2 \sqrt{2} \)
              B.\(2\)
              C.\( \sqrt{2} \)
              D.\(1\)
            • 7.

              直线\(x-y-5=0\) 被圆\({{x}^{2}}+{{y}^{2}}-4x+4y+4=0\) 截得的弦长为      

            • 8.

              在极坐标系中,圆\(\rho =2\cos \theta \)被直线\(\rho \cos \theta =\dfrac{1}{2}\)所截得的弦长为       

            • 9.

              直线\(\begin{cases} & x=1+2t \\ & y=2+t \\ \end{cases}(\)\(t\)为参数\()\)被圆\(x\)\({\,\!}^{2}+\)\(y\)\({\,\!}^{2}=9\)截得的弦长等于        \((\)    \()\)

              A.\(\dfrac{12}{5}\)
              B.\(\dfrac{12}{5}\sqrt{2}\)
              C.\(\dfrac{9}{5}\sqrt{2}\)
              D.\(\dfrac{12}{5}\sqrt{5}\)
            • 10.

              直线\(x-y=0\)被圆\(x^{2}+y^{2}=1\)截得的弦长为\((\)  \()\)

              A.\( \sqrt{2} \)
              B.\(2\)
              C.\(4\)
              D.\(1\)
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