优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知直线\({{l}_{1}}\):\(x=2\),\({{l}_{2}}\):\(3x+5y -30 =0\),点\(p\)为抛物线\(y2= -8x\)上的任一点,则\(p\)到直线\({{l}_{1,}}{{l}_{2}}\)的距离之和的最小值为

              A.\(2\)
              B.\(2\sqrt{34}\)
              C.\(\dfrac{18}{17}\sqrt{34}\)
              D.\(\dfrac{16}{15}\sqrt{34}\)
            • 2. 已知抛物线关于\(x\)轴对称,它的顶点在坐标原点\(O\),并且经过点\(M(2,y_{0}).\)若点\(M\)到该抛物线焦点的距离为\(3\),则\(|OM|=(\)  \()\)
              A.\(2 \sqrt {2}\)
              B.\(2 \sqrt {3}\)
              C.\(4\)
              D.\(2 \sqrt {5}\)
            • 3.

              若抛物线\({y}^{2}=8x \)上一点\(P\)到其焦点的距离为\(9\),则点\(P\)的坐标为\((\)   \()\)。

              A.\(\left(7,± \sqrt{14}\right) \)
              B.\(\left(14,± \sqrt{14}\right) \)
              C.\(\left(7,±2 \sqrt{14}\right) \)
              D.\(\left(-7,±2 \sqrt{14}\right) \)
            • 4.
              直线\(l\)过抛物线\(C\):\(y^{2}=2px(p > 0)\)的焦点且与\(x\)轴垂直,\(l\)与\(C\)交于\(A\)、\(B\)两点,\(P\)为\(C\)的准线上一点,若\(\triangle ABP\)的面积为\(36\),则\(p\)的值为\((\)  \()\)
              A.\(3\)
              B.\(6\)
              C.\(12\)
              D.\(6 \sqrt {2}\)
            • 5.

              设\(AB\)为过抛物线\({{y}^{2}}=2px(p > 0)\)的焦点的弦,则\(\left| AB \right|\)的最小值为(    )

              A.\(\dfrac{p}{2}\)
              B.\(p\)
              C.\(2p\)
              D.无法确定
            • 6.

              若点\(A\)的坐标为\((3,2)\),\(F\)是抛物线\({{y}^{2}}=2x\)的焦点,点\(M\)在抛物线上移动时,使\(\left| MF \right|+\left| MA \right|\)取得最小值的\(M\)的坐标为(    ).

              A.\(\left( 0,0 \right)\)
              B.\(\left( \dfrac{1}{2},1 \right)\)
              C.\(\left( 1,\sqrt{2} \right)\)
              D.\(\left( 2,2 \right)\)
            • 7.

              若抛物线\({{y}^{2}}=8x\)上一点\(P\)到其焦点的距离为\(9\),则点\(P\)的坐标为

              A.\((7,\pm \sqrt{14})\)
              B.\((14,\pm \sqrt{14})\)
              C.\((7,\pm 2\sqrt{14})\)
              D.\((-7,\pm 2\sqrt{14})\)
            • 8.

              抛物线\({x}^{2}= \dfrac{1}{2}y \)在第一象限内图像上的一点\(\left({a}_{i},2{{a}_{i}}^{2}\right) \)处的切线与 \(x\) 轴交点的横坐标记为\({a}_{i+1} \),其中\(i∈{N}^{*} \),若\({a}_{2}=32 \),则\({a}_{2}+{a}_{4}+{a}_{6} \)等于(    )

              A.\(21\)                
              B.\(32\)                   
              C.\(42\)
              D.\(64\)
            • 9. 抛物线\(y=4x^{2}\)上一点到直线\(y=4x-5\)的距离最短,则该点的坐标是\((\)  \()\)
              A.\((1,2)\)
              B.\((0,0)\)
              C.\(( \dfrac {1}{2},1)\)
              D.\((1,4)\)
            • 10.

              过点\(M(\dfrac{\sqrt{2}}{2},-\dfrac{\sqrt{2}}{2})\)作圆\({{x}^{2}}+{{y}^{2}}=1\)的切线\(l\),\(l\)与\(x\)轴的交点为抛物线\(E:{{y}^{2}}=2px(p > 0)\)的焦点,\(l\)与抛物线\(E\)交于\(A,B\)两点,则\(AB\)中点到抛物线\(E\)的准线的距离为\((\)     \()\)

              A.\(4\sqrt{2}\)        
              B.\(3\sqrt{2}\)
              C.\(\dfrac{7\sqrt{2}}{2}\)
              D.\(\dfrac{5\sqrt{2}}{2}\)
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