优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知双曲线\(C:{{x}^{2}}-\dfrac{{{y}^{2}}}{3}=1\)的右顶点为\(A\),过右焦点\(F\)的直线\(l\)与\(C\)的一条渐近线平行,交另一条渐近线于点\(B\),则\({{S}_{\Delta ABF}}=(\)  \()\)

              A.\(\dfrac{3\sqrt{3}}{4}\)
              B.\(\dfrac{3\sqrt{3}}{8}\)
              C.\(\sqrt{3}\)
              D.\(\dfrac{\sqrt{3}}{2}\)
            • 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. 一条光线从点\(A(-2,3)\)射出,经\(x\)轴反射后,反射光线经过点\(B(3,2)\),则反射光线所在的直线方程为 ______ .
            • 4.

              若直线\(l\)\({\,\!}_{1}\):\(y\)\(=\)\(k\)\((\)\(x\)\(-4)\)与直线\(l\)\({\,\!}_{2}\)关于点\((2,1)\)对称,则直线\(l\)\({\,\!}_{2}\)恒过定点\((\)  \()\)

              A.\((0,4)\)                             
              B.\((0,2)\) 
              C.\((-2,4)\)                     
              D.\((4,-2)\)
            • 5.

              直线\(y=mx+2m+1\)恒过一定点,此定点为________.

            • 6. 已知平面内两点\(A(8,-6)\),\(B(2,2)\).

              \((\)Ⅰ\()\)求\(AB\)的中垂线方程;

              \((\)Ⅱ\()\)求过\(P(2,-3)\)点且与直线\(AB\)平行的直线\(l\)的方程;

              \((\)Ⅲ\()\)一束光线从\(B\)点射向\((\)Ⅱ\()\)中的直线\(l\),若反射光线过点\(A\),求反射光线所在的直线方程.

            • 7.

              已知圆\(M\):\((x+ \sqrt{3}a)^{2}+y^{2}=16a^{2}(a > 0)\)及定点\(N( \sqrt{3}a,0)\),点\(P\)是圆\(M\)上的动点,点\(G\)在\(MP\)上,且满足\(|GP|=|GN|\),\(G\)点的轨迹为曲线\(C\).

              \((1)\)求曲线\(C\)的方程;

              \((2)\)若点\(A(1,0)\)关于直线\(x+y-t=0(t > 0)\)对称点在曲线\(C\)上,求\(a\)的取值范围\(.\)                       

            • 8.
              已知直线\(l\):\(kx-y+1-2k=0(k∈R)\)过定点\(P\),则点\(P\)的坐标为 ______ .
            • 9.

              已知点\(A(-1,0)\),\(B(1,0)\),\(C(0,1)\),直线\(y=ax+b(a > 0)\)将\(\triangle ABC\)分割为面积相等的两部分,则\(b\)的取值范围是 (    )

              A.\((0,1)\)  
              B.\(\left( 1\mathrm{{-}}\dfrac{\sqrt{2}}{2}\mathrm{{,}}\dfrac{1}{2} \right)\)
              C.\(\left( 1\mathrm{{-}}\dfrac{\sqrt{2}}{2}\mathrm{{,}}\dfrac{1}{3} \right\rbrack\)
              D.\(\left\lbrack \dfrac{1}{3}\mathrm{{,}}\dfrac{1}{2} \right)\)
            • 10.

              \((1)\)求过点\((2,3)\)且在\(x\)轴和\(y\)轴截距相等的直线的方程_________________.

              \((2)\)已知圆\({{x}^{2}}-4x-4+{{y}^{2}}=0\)上的点\(P(x,y)\),求\({{x}^{2}}+{{y}^{2}}\)的最大值_________________.

              \((3)\)已知圆\({{x}^{2}}+{{y}^{2}}=4\)和圆外一点\(P(-2,-3)\),求过点 \(P\) 的圆的切线方程为________________

              \((4)\)若\(l\)为一条直线,\(\alpha \),\(\beta \),\(\gamma \)为三个互不重合的平面,给出下面四个命题:\(①\alpha ⊥\gamma \),\(\beta ⊥\gamma \),则\(\alpha ⊥\beta \);\(②\alpha ⊥\gamma \),\(\beta /\!/\gamma \),则\(\alpha ⊥\beta \);\(③l/\!/\alpha \),\(l⊥\beta \),则\(\alpha ⊥\beta .④\)若\(l/\!/\alpha \),则\(l\)平行于\(\alpha \)内的所有直线。其中正确命题的序号是 ______\(.(\)把你认为正确命题的序号都填上\()\)

              \((5)\)过点\(P(4,9)\)引圆\({{x}^{2}}+{{y}^{2}}=4\)两条切线\(PA\),\(PB(\)切点为\(A\),\(B)\),则直线\(AB\)方程为_________________

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