解题方法
1 . 如图所示,一隧道内设双行线公路,其截面由长方形的三条边和抛物线的一段构成,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0.5米.
(2)经过点C和焦点的直线l与抛物线交于另一点Q,求
的值;
(3)若行车道总宽度AB为7米,请计算通过隧道的车辆限制高度为多少米(精确到0.1米)?
(2)经过点C和焦点的直线l与抛物线交于另一点Q,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eaf311e61e6f4c16ea84aae4956d2eb.png)
(3)若行车道总宽度AB为7米,请计算通过隧道的车辆限制高度为多少米(精确到0.1米)?
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2 . 已知抛物线
.当过焦点且斜率为
的直线交
于
两点时,
.
(1)求
的标准方程;
(2)若过点
的直线
与
交于
两点,当
时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9602114f45bdcb304e02710ae7bc0e08.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2卷引用:宁夏回族自治区银川市贺兰县第一中学2023-2024学年高二上学期期末复习数学试题(三)
3 . 已知抛物线
的焦点为
,准线为
,过抛物线上一点
作准线的垂线,垂足为
,若
,且
,则
的值为 ____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4494488bdb23f6d941b60af8726993a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce6b638da474cdf44a7d556fd6f4255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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2024-01-11更新
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3卷引用:江苏省2023-2024学年高二上学期期末迎考数学试题(R版B卷)
4 . 已知抛物线
,
为
的焦点,直线
与
交于不同的两点
、
,且点
位于第一象限.
(1)若直线
经过
的焦点
,且
,求直线
的方程;
(2)若直线
经过点
,
为坐标原点,设
的面积为
,
的面积为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0907a673d52825cd7df84b400972d4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5b6926cdb99eb58070b8720718f71a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c525358262126a51fbb598d58f3e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c21cbb1c2bcbcb8391ac5a879f2ae0.png)
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2024-01-06更新
|
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7卷引用:山东省菏泽市定陶区第一中学2023-2024学年高二上学期期末模拟数学试题
5 . 直线
经过抛物线
的焦点,且与抛物线
相交于
两点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c40baffcb91c4d6a69f86a6b6bc5672.png)
A.![]() ![]() |
B.直线![]() ![]() |
C.![]() |
D.以![]() ![]() |
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2024-05-08更新
|
516次组卷
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4卷引用:湖南省长沙市周南中学2023-2024学年高二上学期期末考试数学试题
湖南省长沙市周南中学2023-2024学年高二上学期期末考试数学试题广东省惠州市惠阳区丰湖高级中学2023-2024学年高二下学期5月月考数学试卷云南省昆明市第八中学2023-2024学年高二下学期月考二数学试卷(已下线)2024年新课标全国Ⅱ卷数学真题变式题6-10
解题方法
6 . 已知抛物线C:
,点F为C的焦点,直线l:
与x轴、y轴分别交于A,B两点,若
的面积为12,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915214095e7786e305562acf3c083026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4139b091e9dc432b267ff68420c77de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
A.2 | B.3 | C.4 | D.5 |
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解题方法
7 . 已知直线l:
与抛物线
交于A,B两点.若
,则m的值______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48867e261c61d24a0a1a4f7ff4627c3.png)
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8 . 抛物线
被直线
截得的弦的中点
的纵坐标为1.
(1)求
的值及抛物线的准线方程;
(2)过抛物线的焦点
作两条互相垂直的直线
,
,直线
与拋物线相交于
,
两点,直线
与抛物线相交于
,
两点,求四边形
的面积
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d6e08526a91f8dfd160e7da2f92a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)过抛物线的焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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名校
解题方法
9 . 已知抛物线
的焦点为
,
为
上在第四象限内一点,且
,直线
与
交于
两点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dda1d7b3982b398ffa32f3dbfdfe787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a0328dde917c3e6d0f1ca9ddb6027b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
A.![]() ![]() | B.点![]() ![]() ![]() |
C.![]() ![]() | D.![]() |
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2023-09-26更新
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6卷引用:模块二 专题5 圆锥曲线的定义应用 期末终极研习室高二人教A版
(已下线)模块二 专题5 圆锥曲线的定义应用 期末终极研习室高二人教A版内蒙古鄂尔多斯市西四旗2023-2024学年高二上学期期末数学试题(已下线)模块三 专题3 圆锥曲线的定义的应用(高一人教A)贵州省黔西南州兴义市顶效开发区顶兴学校2023-2024学年高三上学期第二次月考数学试题云南省楚雄市东兴中学2024届高三上学期12月月考数学试题江西省红色十校2024届高三上学期9月联考数学试题
10 . 已知抛物线
的焦点
到双曲线
的渐近线的距离是
.
(1)求抛物线
的方程;
(2)已知过点
的直线与
交于
,
两点,线段
的中垂线与
的准线
交于点
,且线段
的中点为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c42d88e496a17562d25195301e0ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22df7f36d2d26a4624d47e65d675614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25eb5d99a1464a6a05162c49c1f15cd6.png)
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