1 . 已知椭圆
的左右两个焦点分别是
、
,抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0782718dd8b2e591ef21fc89d1af2fb.png)
以
为焦点,点
是椭圆
与抛物线
的交点,若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0782718dd8b2e591ef21fc89d1af2fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75ed10db4b9747a4b6d865b774f6b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53da0d59e182415a90f98c90d1106129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3086880c583bb4a13bb5dd8e46abf2e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
A.![]() ![]() | B.![]() | C.![]() ![]() | D.![]() |
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2 . 已知抛物线
上三点
、
、
,直线
、
是圆
的两条切线,则直线
的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f54dd475ff1321041c80738b201c3b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9df0d79e42d86b0def4caa10dffa75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 已知抛物线
,直线
经过焦点
交
于
两点,其中点
的坐标为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bb7ff5012ac35f2e5fa64b0247ce93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-02-22更新
|
827次组卷
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5卷引用:云南省昆明市行知中学2022-2023学年高二上学期2月月考数学试题
云南省昆明市行知中学2022-2023学年高二上学期2月月考数学试题2023届普通高等学校招生全国统一考试仿真模拟卷数学试题(一)(已下线)专题22 抛物线-1(已下线)专题22 抛物线-3(已下线)3.3.2 抛物线的几何性质(2)
4 . 已知抛物线
(
)上一点M的纵坐标为
,该点到准线的距离为6,则该抛物线的标准方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b929d327ee21d7b778b4b79d1e0eca43.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
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5 . 如图,一隧道内设双行线公路,其截面由一个长方形和抛物线构成.为保证安全,要求行驶车辆顶部(设为平顶)与隧道顶部在竖直方向上高度之差至少要有0.5m,已知行车道总宽度|AB|=6m,那么车辆通过隧道的限制高度约为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/25/88866482-15a7-47b1-a7a3-51dedc7a2137.png?resizew=191)
A.3.1m | B.3.3m | C.3.5m | D.3.7m |
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2023-05-23更新
|
154次组卷
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3卷引用:四川省泸州市2022-2023学年高二上学期期末考试文科数学试题
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解题方法
6 . 已知平面四边形
的四个顶点都在抛物线
上,其中顶点
,
为抛物线的焦点,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb3b9aab72de273ba2f38c9624e94ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5bdf7cb8958e92e750646138ef6b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28fbace94cb1568e92e83b586064dd8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9ef8d6887171e23edad4f90d018c80.png)
A.12 | B.9 | C.6 | D.3 |
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2022-11-10更新
|
1590次组卷
|
3卷引用:3.3.1 抛物线的标准方程(同步练习基础篇)
2023高三·全国·专题练习
7 . 已知
为坐标原点,垂直抛物线
的轴的直线与抛物线
交于
两点,
,则
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc11e7549cfce9220e70250ac943e457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
A.4 | B.3 | C.2 | D.1 |
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8 . 已知函数
且
的图象过定点
,若抛物线
也过点
,则抛物线的准线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327384bddff7425347123bda81086ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-02-03更新
|
444次组卷
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5卷引用:山西省部分学校2022-2023学年高三上学期新高考核心模拟(中)数学试题(二)
9 . 某学习小组研究一种如图1所示的卫星接收天线,发现其曲面与轴截面的交线为抛物线,如图2所示,在轴截面内的卫星信号波束呈近似平行的状态射入,经反射聚焦到焦点
处,从而位于焦点处的信号接收器可以接受到较强的信号波.已知卫星接收天线的口径(直径)为
,深度为
,则该卫星接收天线轴截面所在的抛物线的焦点到顶点的距离为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/14d762ea-057d-4af7-b903-adb9f8f1e7df.png?resizew=233)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c470099006b021d5fe81c85c5e3639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f328ba89c0a92a4447788b65571f7aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/14d762ea-057d-4af7-b903-adb9f8f1e7df.png?resizew=233)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知
为坐标原点,抛物线
与曲线
交于点
,其横坐标为4,记
的平行于
的切线为
的平行于
的切线为
,则下列判断错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310a72816188ba54fd532459517a3327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fa3749c9c117a21a4a0673e43cf9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
A.![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2023-01-18更新
|
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2卷引用:河南省九师联盟2022-2023学年高三上学期12月月考理科数学试题