名校
解题方法
1 . 已知抛物线C:
的焦点为F,过点F的直线l与抛物线C交于A,B两点,O为坐标原点,直线
过点A且与OA垂直,直线
过点B且与OB垂直,直线
与
相交于点Q,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
A.设AB的中点为H,则![]() |
B.点Q的轨迹为抛物线 |
C.点Q到直线l距离的最小值为![]() |
D.![]() ![]() |
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3卷引用:吉林省通化市梅河口市第五中学2024届高考模拟预测数学试题
21-22高二·江苏·单元测试
2 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fe9059acc47d2447576e1260c4622.png)
的左、右焦点分别是
,
,点
到直线
的距离为
,若点
在椭圆
上,
的周长为6.
(1)求椭圆
的方程;
(2)若过
的直线
与椭圆
交于不同的两点
,
,求
的内切圆的半径的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fe9059acc47d2447576e1260c4622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b961597f2495a875b71f8a2f2eff69.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05063aa8290b34b56ac3b6193cba95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bb8ca50f11fb7f9c2b96fd42b11a28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d617aaa770c4e05893a1e4458f43d3bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d617aaa770c4e05893a1e4458f43d3bd.png)
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead68be1b467506dcdcd0c90317f44b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d617aaa770c4e05893a1e4458f43d3bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b5ebfc6a82f19cea0fd940017acf7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5fcfc55b56f04ac530871067e5ce71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b5c81ee16e93e9822c4dc54c362cb3.png)
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3 . 已知函数
的图象在点
处的切线与直线
垂直.
(1)判断
的零点的个数,并说明理由;
(2)证明:
对
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d8c42c314a07da5e495a1280253ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1a686b80b8f109a929f58c2de7201d.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02e32435aa5b57a34ed4a39b07c5530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc4136bd17997e11a7f8abcb19f9018.png)
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2020-07-21更新
|
485次组卷
|
4卷引用:吉林省示范高中(四平一中、梅河口五中、白城一中等)2020届高三第四次模拟考试数学(理)试题
4 . 直线
过点
且与抛物线
交于
,
(
,
都在
轴同侧)两点,过
,
作
轴的垂线,垂足分别为
,
.
(1)若
,
,证明:
的斜率为定值.
(2)若
,设
的面积为
,梯形
的面积为
,是否存在正整数
,使
成立?若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1208e24cb1d3ae6a50f161b970ec2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37919582436fc6857490669e562554cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0664eee3c4475b5391da240931f0a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea51de5ca1c2879e7a767a60ce4624cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2397d5e67a3e0adc6d9000450f1651ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2020-07-21更新
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2卷引用:吉林省示范高中(四平一中、梅河口五中、白城一中等)2020届高三第四次模拟考试数学(理)试题
名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d889069ca94e0339f85b84ce01047943.png)
(1)若
,试讨论
的单调性;
(2)若对
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d889069ca94e0339f85b84ce01047943.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9511cd8efdb9eb9045c8f73f2c231c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-04-18更新
|
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|
4卷引用:2020届吉林省吉林市高三第三次调研测试(4月) 数学(文)试题
2020届吉林省吉林市高三第三次调研测试(4月) 数学(文)试题辽宁省辽河油田第二高级中学2020届高三6月模拟考试数学(文)试题(已下线)理科数学-2020年高考押题预测卷03(新课标Ⅱ卷)《2020年高考押题预测卷》(已下线)文科数学-2020年高考押题预测卷03(新课标Ⅱ卷)《2020年高考押题预测卷》
6 . 已知函数
,若实数
满足
,
,则
的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f19eb678d4c0b9ab9c7204ea172b66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f80045c953d00cd5f0af06fb3752279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
您最近一年使用:0次
名校
解题方法
7 . 已知倾斜角为
的直线经过抛物线
的焦点
,与抛物线
相交于
、
两点,且
.
(1)求抛物线
的方程;
(2)求过点
且与抛物线
的准线相切的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c348601813d70ba64ffca73cf2256f3.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2020-04-18更新
|
522次组卷
|
2卷引用:2020届吉林省吉林市高三第三次调研测试(4月) 数学(文)试题
名校
解题方法
8 . 已知函数
,
.若存在
,
使得
成立,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f53f81bca037a4383c1fab122a3cd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6b0fdccf03ed7b58bda53523ac9b4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e300e60be8d1827744cdc01e7d04c840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ba8542fbe02e78cf3948c9abea9855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def8b5217a949f06e4afe6847dbeb7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5fd72f3b9d868ca580e09da1d79e51.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2020-04-10更新
|
2119次组卷
|
16卷引用:吉林省长春市八中2020届高三第二次诊断性检测数学(理)试题
吉林省长春市八中2020届高三第二次诊断性检测数学(理)试题2020届四川省成都市高三第二次诊断性检测理科数学试题(已下线)文科数学-2020年高考押题预测卷01(新课标Ⅱ卷)《2020年高考押题预测卷》(已下线)理科数学-2020年高考押题预测卷01(新课标Ⅱ卷)《2020年高考押题预测卷》四川省泸州市泸县第四中学2020-2021学年高三上学期开学考试数学(文)试题四川省泸州市泸县第四中学2020-2021学年高三上学期开学考试数学(理)试题(已下线)调研测试二(A卷 基础过关检测)-2021年高考数学(理)一轮复习单元滚动双测卷(已下线)调研测试五(B卷 滚动提升检测)-2021年高考数学(理)一轮复习单元滚动双测卷河南省信阳市2020-2021学年高二下学期期末数学(理)试题四川省成都市第十二中学2020-2021学年高二下学期期中数学试题湖北省重点高中智学联盟2021-2022学年高二下学期5月联考数学试题湖南省张家界市慈利县第一中学2022-2023学年高三上学期第四次月考数学试题广西壮族自治区钦州市第四中学2023届高三上学期11月考试数学(理)试题(已下线)专题08 导数与函数综合压轴(选填题)-1(已下线)模块三 大招3 同构思想(已下线)第03讲 导数与函数的极值、最值(七大题型)(练习)
名校
解题方法
9 . 已知函数
.
(1)求不等式
的解集;
(2)设函数
的最小值为m,当a,b,
,且
时,求
的最大值.
![](https://img.xkw.com/dksih/QBM/2020/3/9/2415737295060992/2416062545199104/STEM/34c49c58bd714133920bb56a98d7f14a.png?resizew=177)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4509817be39bef4bcde115996ee39e8.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac49619543ace1f24754240fcf6cb09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d86be2de99fbf7f99cd54ab399146b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e644e75022aa5372e81410c95f393b10.png)
您最近一年使用:0次
2020-03-09更新
|
991次组卷
|
15卷引用:【市级联考】吉林省长春市普通高中2019届高三质量检测(三)数学(理)试题
【市级联考】吉林省长春市普通高中2019届高三质量检测(三)数学(理)试题【市级联考】吉林省长春市普通高中2019届高三质量检测(三)数学(文科)试题【省级联考】东北三省四市2019届高三第一次模拟数学(文)试题【市级联考】东北三省四市2019届高三第一次模拟数学(理)试题1【市级联考】辽宁省大连市2019届高三第一次模拟考试数学(理)试题【市级联考】东北三省四市2019届高三第一次模拟数学(理)试题2【市级联考】东北三省四市2019届高三第一次模拟数学(文)试题2020届湖南省长沙市长郡中学高三下学期4月第三次适应性考试数学(文)试题江西省南昌市第二中学2019-2020学年高三第四次月考数学(文)试题2020届四川省泸县第一中学高三下学期第一次在线月考数学(理)试题2020届四川省泸县第一中学高三下学期第一次在线月考数学(文)试题河北省石家庄市第二中学(南校区)2019-2020学年高三下学期教学质量检测模拟数学(理)试题(已下线)理科数学-2020年高考押题预测卷03(新课标Ⅱ卷)《2020年高考押题预测卷》(已下线)文科数学-2020年高考押题预测卷03(新课标Ⅱ卷)《2020年高考押题预测卷》(已下线)专题23 不等式选讲-2020年高考数学(文)母题题源解密(全国Ⅲ专版)
名校
10 . 在平面直角坐标系
中,已知椭圆
的左顶点为
,右焦点为
,
,
为椭圆
上两点,圆
.
(1)若
轴,且满足直线
与圆
相切,求圆
的方程;
(2)若圆
的半径为2,点
,
满足
,求直线
被圆
截得弦长的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3285a2383fa18025034cf9876175295.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b1da9046b4cb82135a4a1eaa528c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/29f0a238b82b975661d2df743acffdad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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4卷引用:2020届吉林省梅河口市第五中学高三下学期模拟考试数学(文)试题