1 . 已知椭圆C:
过点
,直线
与椭圆
交于
两点,且线段
的中点为
为坐标原点,直线
的斜率为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a1baa2dbbdb3bca1776d10b288cd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73533688e2820dacba2199ba6087bd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876f208635a511c8dc89da1dad21c868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
A.![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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解题方法
2 . 在表面积为
的球O的球面上存在A,B,C三点,且
,
,E为线段OC的中点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a39dce3f1e36dbe01293c309816968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306b21a5d7e68f1992e5797b4368ed56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397d16b4a33ef2ef92cf7adb5674ec60.png)
A.![]() |
B.异面直线![]() ![]() ![]() |
C.若点O到平面![]() ![]() ![]() ![]() ![]() |
D.若点O到平面![]() ![]() ![]() ![]() |
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3 . 椭圆
的左右焦点分别为
,若P,Q为椭圆C上两点,命题p:椭圆C的离心率
.则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e756feec2851b90497421790a7206e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
A.命题a:![]() ![]() ![]() ![]() |
B.命题b:![]() ![]() |
C.命题c:![]() ![]() ![]() |
D.命题d:![]() ![]() ![]() |
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4 . 已知函数
.
(1)当
时,求
的单调区间;
(2)若
时,
,求a的取值范围;
(3)对于任意
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27862c9517dbb4eb17a6725eb142969.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(3)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af027bd16e380d3be03a9761ca56055.png)
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2024-01-18更新
|
2007次组卷
|
9卷引用:辽宁省沈阳市、大连市2023-2024学年高二上学期教学联盟大联考数学试题
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解题方法
5 . 若椭圆
和
的方程分别为
和
(
且
)则称
和
为相似椭圆.己知椭圆
,过
上任意一点P作直线交
于M,N两点,且
,则
的面积最大时,
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b6494c8078692621054e98b8d0d874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9501c4c1f12367e5edc6f1f6e3c94c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472393b18c7880e73b40e31fbe2d951c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98a8dc70ef391b5da94772c412d4f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234ca137f313c1286afd25c1f0536e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-17更新
|
2230次组卷
|
5卷引用:辽宁省大连市2023-2024学年高二上学期期末数学试题
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解题方法
6 . 已知函数
(
为自然对数的底数).
(1)若
,求实数
的值;
(2)证明:
;
(3)对
恒成立,求
取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da80426b4a667a7e2d5073408da1dbaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dce060801a5814dd2c812c578581e88.png)
(3)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a08c1678252718ea5cc727d476920fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-01-16更新
|
917次组卷
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3卷引用:辽宁省大连市2024届高三上学期双基测试数学试题
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7 . 已知椭圆
,双曲线
(
,
),椭圆
与双曲线
有共同的焦点,离心率分别为
,
,椭圆
与双曲线
在第一象限的交点为
且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8210484dd6815b5bebc7b22f1389cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ab2caccd742eb636bd8378661a8807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b967232e28ad0d453adc66676bdf8b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f1ea30341eb5d584710c3aebc64ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7285470bf401f5edaac641234ee6ff6a.png)
A.若![]() ![]() |
B.![]() ![]() |
C.![]() ![]() ![]() ![]() ![]() |
D.![]() ![]() ![]() ![]() ![]() ![]() |
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2024-01-15更新
|
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8 . 已知函数
.
(1)讨论
的单调性;
(2)若
恰好有两个零点
,
,且
恒成立,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e107063f2300c028d91537c0cf70832a.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfab5631d1543bf2090b1c506698ee35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ed3f472299563e31282a44aa9fe202.png)
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|
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4卷引用:辽宁省抚顺市六校协作体2024届高三上学期期末数学试题
辽宁省抚顺市六校协作体2024届高三上学期期末数学试题江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(九)(已下线)专题10 导数12种常见考法归类(5)(已下线)模块2专题7 对数均值不等式 巧妙解决双变量练
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解题方法
9 . 已知双曲线
的对称轴为坐标轴,以坐标原点
为对称中心,且过点
,
.
(1)求双曲线
的方程;
(2)
,
,
为双曲线
上不同三点,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2719ce8a1c0aaa60da102db5712d63e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d5bd66a1bc9779b20137ad9676526b.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b820093c501306e7887dff633409c89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
10 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbf98ce94d2f309bf5c7d626a0d33ed.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() |
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