1 . 已知椭圆
的右焦点为
,其四个顶点的连线围成的四边形面积为
;菱形
内接于椭圆
.
(1)求椭圆
的标准方程;
(2)(ⅰ)坐标原点
在边
上的投影为点
,求点
的轨迹方程;
(ⅱ)求菱形
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)(ⅰ)坐标原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/dad2a36927223bd70f426ba06aea4b45.png)
(ⅱ)求菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
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2 . 已知直线
与函数
的图象相切,则函数
的图象在
处的切线与坐标轴围成的三角形的面积的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4605f24d585d1589fa00ca53e9b6ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2b4a486bc057f77636b40e5b6bace7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 定义:若函数
图象上恰好存在相异的两点
满足曲线
在
和
处的切线重合,则称
为曲线
的“双重切点”,直线
为曲线
的“双重切线”.
(1)直线
是否为曲线
的“双重切线”,请说明理由;
(2)已知函数
求曲线
的“双重切线”的方程;
(3)已知函数
,直线
为曲线
的“双重切线”,记直线
的斜率所有可能的取值为
,若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ece491f9ba053a2ead5ad54138d779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d430e6eb5f8b43723db095937fbc74f7.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5776b27d76690a67770d954a47bfb0f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6f04900fb8400a415b1067320a2f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e540ef465ca68c186cc972d54d3a268e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6b9ccddda8585a04f8ab4d4b4583a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a097fa8e3bfa45de1ea35f1ad907fe3.png)
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2024-04-17更新
|
1265次组卷
|
6卷引用:河北省邢台市2024届高三下学期教学质量检测(一)数学试题
河北省邢台市2024届高三下学期教学质量检测(一)数学试题广西2024届高三4月模拟考试数学试卷(已下线)模块五 专题5 全真拔高模拟5(苏教版高二期中研习)辽宁省辽阳市2023-2024学年高三下学期二模数学试卷(已下线)专题16 对数平均不等式及其应用【练】(已下线)拔高点突破05 函数与导数背景下的新定义压轴解答题(九大题型)
名校
解题方法
4 . 已知圆
.点
在圆
上,延长
到
,使
,点
在线段
上,满足
.
(1)求点
的轨迹
的方程;
(2)设
点在直线
上运动,
.直线
与
与轨迹
分别交于
两点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2b4e2069ce7df182d108413ec76248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/625afdec90efb719adb35a69bbb6a70e.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/ca45dca68eb243a0d5e03407d3eb00b4.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b36cb65b9e164898dd2ee182b65401f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ee6b3f3582c4da0fdcf1c9ffdde109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26960eb7fa677ced9fd81c22a79984ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f3ed5ea1cf0fa8f7c6be46cd5fa057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa2947ec9518014cf7fe409629553618.png)
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2024高三·全国·专题练习
5 . 已知O为坐标原点,抛物线
,过点
的直线交抛物线于A,B两点,
.
(1)求抛物线C的方程;
(2)若点
,连接AD,BD,证明:
;
(3)已知圆G以G为圆心,1为半径,过A作圆G的两条切线,与y轴分别交于点M,N且M,N位于x轴两侧,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a1eb1babf5a1eb0f95f3af5c53fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15aab800f41f7a47bde139498e19d294.png)
(1)求抛物线C的方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ab82c33e6c1f8b73628fa78e6868b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c210f0bb0b964d8b059fdea307a90f.png)
(3)已知圆G以G为圆心,1为半径,过A作圆G的两条切线,与y轴分别交于点M,N且M,N位于x轴两侧,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
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2024-04-08更新
|
2095次组卷
|
6卷引用:河北省沧州市2024届高三下学期6月保温考试数学试卷
河北省沧州市2024届高三下学期6月保温考试数学试卷(已下线)2024年普通高等学校招生全国统一考试数学文科猜题卷(七)湖北省黄冈市浠水县第一中学2024届高三下学期第三次高考模拟数学试题(已下线)数学(新高考卷03,新题型结构)(已下线)压轴题02圆锥曲线压轴题17题型汇总-2重庆市渝北中学校2023-2024学年高三下学期5月月考质量监测数学试题
解题方法
6 . 已知平面内定点
是以
为直径的圆
上一动点(
为坐标原点).直线
与点
处
的切线交于点
,过点
作
轴的垂线
,垂足为
,过点
作
轴的垂线
,垂足为
,过点
作
的垂线
,垂足为
.
(1)求点
的轨迹方程
;
(2)求矩形
面积的最大值;
(3)设
的轨迹
,直线
与
轴围成面积为
,甲同学认为随
的增大,
也会达到无穷大,乙同学认为随
的增大
不会超过4,你同意哪个观点,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d89c84f89fdb91c6ea75281afb0a835.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.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/7f9e8449aad35c5d840a3395ea86df6d.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/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)求矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec780e86f57790cf88ec761e219bf5f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fbf172a91af29e4e1b736014ee9f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
7 . 已知抛物线C:
的焦点为
,点
在抛物线C上,则( )
![](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/7789a500686c7a73770404ead6af0590.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-04-07更新
|
2267次组卷
|
7卷引用:河北省重点高中2024届高三下学期5月模拟考试数学试题(一)
河北省重点高中2024届高三下学期5月模拟考试数学试题(一)河南省信阳市第一高级中学(华大新高考联盟)2024届高三4月教学质量测评数学试题湖北省华中师范大学第一附属中学、湖南省湖南师范大学附属中学等三校2024届高三下学期4月模拟考试(二模)数学试卷河南省信阳市信阳高级中学2024届高三下学期4月二模数学试题(已下线)专题6 学科素养与综合问题(多选题11)辽宁省辽阳市辽阳县辽阳石油化纤公司高级中学2024届高三下学期模拟考试数学试题(已下线)专题7 圆锥曲线与定比分点法【讲】(压轴小题大全)
名校
8 . 已知函数
.
(1)讨论
的单调性;
(2)若
恒成立,求
的取值集合;
(3)若存在
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57fb6e0db82c11dbf6d4a022b12dcbd4.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb948b7736245b30c44ef9270da0f88f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a78f37a26bad9bcd4165fedc05ce56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-04-02更新
|
714次组卷
|
5卷引用:河北省涞源县第一中学等部分高中2024届高三下学期三模考试数学试题
9 . 已知函数
,
.
(1)求曲线
在点
处的切线方程.
(2)已知关于
的方程
恰有4个不同的实数根
,其中
,
.
(i)求
的取值范围;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6233814cb71490dee2b31b2ed87225a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)已知关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1146b920e21e9b2bf1bb5df6afe7fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6270bb08b90f72d5671ab8225f356c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574824d85f44d42246529ac135c0391c.png)
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名校
解题方法
10 . 已知函数
.
(1)当
时,求函数
的单调区间和极值;
(2)当
时,不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9051c82f5a34a4635202f3fe72e32fdc.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce6227807fd76d382863bff2f89ef80.png)
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