优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知点\(P\)在直线\(x+2y-1=0\)上,点\(Q\)在直线\(x+2y+3=0\)上,\(PQ\)的中点为\(M(x_{0},y_{0})\),且\(y_{0} > x_{0}+2\),则\(\dfrac{{{y}_{0}}}{{{x}_{0}}}\)的取值范围是

              A.\(\left( \dfrac{1}{5},1 \right)\)
              B.\(\left( -\dfrac{1}{2},\dfrac{1}{5} \right)\)
              C.\(\left( -1,-\dfrac{1}{5} \right)\)
              D.\(\left( -\dfrac{1}{2},-\dfrac{1}{5} \right)\)
            • 2.

              已知点\(A\),\(B\)在抛物线\(y^{2}=4x\)上,弦\(AB\)的中点为\(M(\dfrac{3}{2},1)\),则弦\(AB\)的长度为

              A.\(4\)
              B.\(5\)
              C.\(6\)
              D.\(\dfrac{9}{2}\)
            • 3.

              已知\(A\),\(B\)两点的极坐标为\(\left(6, \dfrac{π}{3}\right) \)和\(\left(8, \dfrac{4π}{3}\right) \),则线段\(AB\)中点的直角坐标为\((\)  \()\)

              A.\(\left( \dfrac{1}{2},- \dfrac{ \sqrt{3}}{2}\right) \)
              B.\(\left(- \dfrac{ \sqrt{3}}{2}, \dfrac{1}{2}\right) \)
              C.\(\left( \dfrac{ \sqrt{3}}{2},- \dfrac{1}{2}\right) \)
              D.\(\left(- \dfrac{1}{2},- \dfrac{ \sqrt{3}}{2}\right) \)
            • 4.

              已知点\(M(4,9)\),\(N(6,3)\), 则以线段\(MN\)为直径的圆的方程为__________________.

            • 5.

              \((1)\)已知\(\alpha\)是第二象限角,化简\(\sqrt{\dfrac{1{+}\sin\alpha}{1{-}\sin\alpha}}{-}\sqrt{\dfrac{1{-}\sin\alpha}{1{+}\sin\alpha}}\)的结果是______ .

              \((2)\)已知函数\(f(x){=}a^{x{+}1}{+}1(a{ > }0{,}a{\neq }1)\),则它的图象恒过定点的坐标为______ .

              \((3)\)已知\(A({-}3{,}2){,}\overrightarrow{{AB}}{=}(6{,}0)\),则线段\(AB\)中点的坐标是______ .

              \((4)\)如图,在正方形\(ABCD\)中,\(E\)为\(BC\)边中点,若\(\overrightarrow{{AE}}{=}\lambda\overrightarrow{{AB}}{+}\mu\overrightarrow{{AD}}\),则\(\lambda{+}\mu{=}\) ______ .

            • 6.

              已知直线\(l_{1}\):\(2x+4y-1=0\)和点\(A(3,0)\),设过点\(A\)且与\(l_{1}\)平行的直线为\(l_{2}\).

              \((1)\)求直线\(l_{2}\)的方程;

              \((2)\)求点\(A(3,0)\)关于直线\(l_{1}\)的对称点\(B\)的坐标.

            • 7.

              已知\(\Delta ABC\)的三个顶点坐标分别为\(A\left( -1,1 \right),B\left( 7,-1 \right),C\left( -2,5 \right),AB\)边上的中线所在直线为\(l\).

              \((\)Ⅰ\()\)求直线\(l\)的方程;

              \((\)Ⅱ\()\)若点\(A\)关于直线\(l\)的对称点为\(D\),求\(\Delta BCD\)的面积.

            • 8.

              已知点\(P(3,a)\),若圆\(O:{x}^{2}+{y}^{2}=4 \)上存在点\(A\),使得线段\(PA\)的中点也在圆\(O\)上,则\(a\)的取值范围是

              A.\(\left( -3\sqrt{3},3\sqrt{3} \right)\)
              B.\(\left[ -3\sqrt{3},3\sqrt{3} \right]\)
              C.\((-2,2)\)
              D.\(\left[ -2,2 \right]\)
            • 9.

              直线\(y=2x+1\)关于点\((1,1)\)对称的直线方程是____________

            • 10.

              已知线段\(AB\)的端点\(A\)的坐标为\((4,3)\),端点\(B\)是圆\(O:{{(x-4)}^{2}}+{{(y-1)}^{2}}=4\) 上的动点.

              \((1)\)求过\(A\)点且与圆\(O\)相交时的弦长为\(2\sqrt{3}\)的直线\(l\)的方程;

              \((2)\)求线段\(AB\)中点\(M\)的轨迹方程,并说明它是什么图形.

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