1 . 已知抛物线
的焦点为
,经过
的直线
与抛物线
交于
两点,设点M在抛物线的准线上,若
是等腰直角三角形,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5473350dacb51280e3b9779c8201d544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
您最近一年使用:0次
2024-01-15更新
|
296次组卷
|
4卷引用:四川省成都外国语学校2023-2024学年高三上学期期末考试理科数学试题
四川省成都外国语学校2023-2024学年高三上学期期末考试理科数学试题上海市建平中学2023-2024学年高二上学期期末质量监测数学试卷(已下线)专题04 圆锥曲线(六大题型+优选提升题)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)上海市上海中学东校2023-2024学年高二下学期5月月考数学试卷
名校
解题方法
2 . 已知抛物线
的焦点为
,过点
的直线
交抛物线于
两点,
的中点为
,以
为直径的圆与
轴交于
两点,当
取最大值时,此时![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477fddf837d4fd6b5afb4cc65bccac04.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45a8a837c11c07073da3ff751d70278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477fddf837d4fd6b5afb4cc65bccac04.png)
您最近一年使用:0次
2024-01-07更新
|
959次组卷
|
3卷引用:贵州省贵阳市第一中学2023-2024学年高三上学期高考适应性月考(四)(12月)数学试题
2023高三·全国·专题练习
3 . 抛物线的弦与过弦端点的两条切线所围成的三角形被称为阿基米德三角形.设抛物线为
,弦AB过焦点,
为阿基米德三角形,则
的面积的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
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2023-10-31更新
|
586次组卷
|
4卷引用:第七节 抛物线 第二课时 直线与抛物线的位置关系 核心考点集训
(已下线)第七节 抛物线 第二课时 直线与抛物线的位置关系 核心考点集训(已下线)3.3.2 抛物线的简单的几何性质(AB分层训练)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)专题25 抛物线的几何性质5种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)(已下线)专题1 千年古图 巧用定理 练
名校
解题方法
4 . 已知抛物线
的焦点为
,过点
的直线交
于
两个不同点,则下列结论正确的是______ .
①若点
,则
的最小值是3
②
的最小值是2
③若
,则直线
的斜率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95cd89f3322b212a357d9eb7f5f53cb.png)
④过点
分别作抛物线
的切线,设两切线的交点为
,则点
的横坐标为
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
①若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bd4e5049fa304e4d352bfe6dee455d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32390a6d8c99da47b13e946c7434dffb.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d669abbef80895dba633950d22c7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95cd89f3322b212a357d9eb7f5f53cb.png)
④过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
您最近一年使用:0次
5 . 已知抛物线
,弦
过抛物线的焦点
,过两点
分别作准线
的垂线,垂足分别为
、
,设
的中点为
,线段
的垂直平分线交
轴于
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c14e7ddebf1abbd0486c4e45c3bae2.png)
______ ;若
的中点为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d624b3aeff8deb12cba1863fd06b1432.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c14e7ddebf1abbd0486c4e45c3bae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d624b3aeff8deb12cba1863fd06b1432.png)
您最近一年使用:0次
2023-03-31更新
|
1593次组卷
|
4卷引用:湖北省十一校2023届高三下学期第二次联考数学试题
名校
解题方法
6 . 已知抛物线
的焦点为F,准线交x轴于点D,过点F作倾斜角为
(
为锐角)的直线交抛物线于A,B两点,如图,把平面
沿x轴折起,使平面
平面
,则三棱锥
体积为__________ ;若
,则异面直线
,
所成角的余弦值取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d62d30d732c3c6ee3f0dd66d7059356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b635e62c3b1f4a57feac8d22be84ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75432478427b7943ee0202da3796a693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
您最近一年使用:0次
2023-03-13更新
|
857次组卷
|
5卷引用:重庆市2023届高三第七次质量检测数学试题
重庆市2023届高三第七次质量检测数学试题重庆市南开中学校2023届高三第七次质量检测数学试题(已下线)模块六 专题8 易错题目重组卷(重庆卷)湖南省岳阳市第一中学2024届高三下学期高考适应性考试数学试题(已下线)第8题 由空间距离求夹角(压轴小题)
7 . 已知抛物线E:
的焦点为F,现有不同的三点A,B,C在抛物线E上,且
,
,则p的值是____________ ;若过点
的直线PM,PN分别与抛物线E相切于点M,N,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf4b92c913e1bf1c2e1ca8e079d5f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af67c65ac0551549865fd6dc07bba4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8902bff3e60ecebdcd71bb2ee8bb97b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
您最近一年使用:0次
2023·全国·模拟预测
名校
8 . 已知A,B,C,D为抛物线
上不同的四点,直线AB,CD交于点
,直线AD经过E的焦点F,若直线AD的斜率为直线BC斜率的4倍,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c42d88e496a17562d25195301e0ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e0b4cce429003557b051ea0fa2f7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
您最近一年使用:0次
9 . 已知抛物线
,过其焦点
的直线
与抛物线
交于P,Q两点(点P在第一象限),
,则直线
的斜率为______ 若
,点
为抛物线
上的动点,且点
在直线
的左上方,则
面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3520a32741ec83b37a30d68b30c759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f05fc6915220cf15717ff47b31c33e.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
您最近一年使用:0次
2023-02-08更新
|
411次组卷
|
3卷引用:重庆市綦江南州中学校2022-2023学年高二上学期期末数学试题
名校
解题方法
10 . 抛物线
的焦点为
,过
的直线交
于
两点,
在
两点处的切线交于点
,则弦
的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5253738504ebbdb51cb6b72caf7fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171e6bcad8bd945b680e048bb1a4376e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-01-01更新
|
568次组卷
|
2卷引用:江苏省淮安市郑梁梅高级中学2023届高三二模数学试题