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名校
解题方法
1 . 已知点
,动点
满足
.
(1)求点
的轨迹
的方程;
(2)若轨迹
的左右顶点分别为
,直线
与直线
交于点
,直线
与轨迹
交于相异的两点
,当点
不在
轴上时,分别记直线
与
的斜率为
,
,求证:
是定值.
![](/uploads/image/squformula/5f867fdf38b4b782f981edaa73f9283c.png)
![](/uploads/image/squformula/dad2a36927223bd70f426ba06aea4b45.png)
![](/uploads/image/squformula/f595683f69d5d6b5ca76408b0ff6ff17.png)
(1)求点
![](/uploads/image/squformula/dad2a36927223bd70f426ba06aea4b45.png)
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若轨迹
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
![](/uploads/image/squformula/01c74a907dda6bb7d9d56d009d9df253.png)
![](/uploads/image/squformula/b11449658adfc07dcf4fc0b25e7ed7c9.png)
![](/uploads/image/squformula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](/uploads/image/squformula/ac047e91852b91af639feec23a9598b2.png)
![](/uploads/image/squformula/d50703c46b6153945d718b198f03b4b5.png)
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
![](/uploads/image/squformula/f54ea1c0c4903b3222aad364b52b5f15.png)
![](/uploads/image/squformula/dad2a36927223bd70f426ba06aea4b45.png)
![](/uploads/image/squformula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](/uploads/image/squformula/20a541b81584a032f571159ea152c85a.png)
![](/uploads/image/squformula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](/uploads/image/squformula/6defc43285a40f7ccb74c1cc04265eba.png)
![](/uploads/image/squformula/423b7ae39db552e60ee8b1d27312306f.png)
![](/uploads/image/squformula/a2a3f348a942d468f0d77c0dfbb41d87.png)
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名校
解题方法
2 . 已知曲线
在点
处的切线与曲线
相切于点
,则下列结论正确的是( )
![](/uploads/image/squformula/b743bb6d5af217588221654a31dbc432.png)
![](/uploads/image/squformula/8198c3b302b3820e86763428eb1e91cc.png)
![](/uploads/image/squformula/31109bde2b310c87e3e7992304765b85.png)
![](/uploads/image/squformula/3463ced6030af957f13f9ba05b977c1c.png)
a.函数![]() |
b.函数![]() ![]() |
c.![]() |
d.![]() |
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解题方法
3 . 已知函数
满足:
,
,,
,
,则( )
![](/uploads/image/squformula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](/uploads/image/squformula/32e837bb2555b79c3374f6c509c8fba5.png)
![](/uploads/image/squformula/3276b5e12396fc4753eb3f8254f9fa68.png)
![](/uploads/image/squformula/e61c9a7ed0961f8977a21dab37aab396.png)
![](/uploads/image/squformula/5fff070e0fe24cd03e682864ab20ccbe.png)
a.![]() | b.![]() |
c.方程![]() | d.![]() ![]() |
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1卷引用:浙江省温州市2023-2024学年高一上学期期末教学质量统一检测数学试题(a卷)
解题方法
4 . 在平面直角坐标系
中,点
,点a为动点,以线段
为直径的圆与
轴相切,记a的轨迹为
,直线
交
于另一点b.
(1)求
的方程;
(2)
的外接圆交
于点
(不与o,a,b重合),依次连接o,a,c,b构成凸四边形
,记其面积为
.
(i)证明:
的重心在定直线上;
(ii)求
的取值范围.
![](/uploads/image/squformula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](/uploads/image/squformula/1f449cadb49859b80c31ef1f68bfe81b.png)
![](/uploads/image/squformula/20a541b81584a032f571159ea152c85a.png)
![](/uploads/image/squformula/d053b14c8588eee2acbbe44fc37a6886.png)
![](/uploads/image/squformula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](/uploads/image/squformula/20a541b81584a032f571159ea152c85a.png)
![](/uploads/image/squformula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求
![](/uploads/image/squformula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)
![](/uploads/image/squformula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](/uploads/image/squformula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
![](/uploads/image/squformula/3ea16ceca816f7d3d50650af141baf42.png)
![](/uploads/image/squformula/cf231f8f86fb922df4ca0c87f044cec3.png)
(i)证明:
![](/uploads/image/squformula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(ii)求
![](/uploads/image/squformula/cf231f8f86fb922df4ca0c87f044cec3.png)
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多选题
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较难(0.4)
|
名校
解题方法
5 . 已知
,
,则( )
![](/uploads/image/squformula/f0fbf42166dd337c577c30499cf4ab73.png)
![](/uploads/image/squformula/cf7ac0d3afc272b2c6624119924040e6.png)
a.当![]() ![]() |
b.当![]() ![]() ![]() |
c.当![]() ![]() ![]() |
d.当![]() ![]() ![]() |
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2024高三·全国·专题练习
解题方法
6 . 已知,且
,求证:
.
![](/uploads/image/squformula/26d8dafc71b106f39f4e15442220897b.png)
![](/uploads/image/squformula/6d550b4316cdaf6d36ecb9254fc69f7b.png)
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(已下线)专题2-6 导数大题证明不等式归类-3
解题方法
7 . 已知如图,点
为椭圆
的短轴的两个端点,且
的坐标为,椭圆
的离心率为.
![](/uploads/image/idqe2124/acef4fa0-271a-4bd0-814d-7deb9069cc85.png)
(1)求椭圆
的标准方程;
(2)若直线
不经过椭圆
的中心,且分别交椭圆
与直线
于不同的三点
(点
在线段
上),直线
分别交直线
于点
.求证:四边形
为平行四边形.
![](/uploads/image/squformula/04d468be20b4d43f5de75416de20e8ee.png)
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
![](/uploads/image/squformula/43a71fc9c0068109dad1382354570665.png)
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
![](/uploads/image/idqe2124/acef4fa0-271a-4bd0-814d-7deb9069cc85.png)
(1)求椭圆
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](/uploads/image/squformula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
![](/uploads/image/squformula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](/uploads/image/squformula/6684304a7537da9517c889c9cbf90a48.png)
![](/uploads/image/squformula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](/uploads/image/squformula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](/uploads/image/squformula/ef49a3ca580a144cc65a609c167facc1.png)
![](/uploads/image/squformula/14d0ff4224f475ab37c6f96d00506f69.png)
![](/uploads/image/squformula/7789a500686c7a73770404ead6af0590.png)
![](/uploads/image/squformula/0d107710e7aff959395ca6f8d23c52c7.png)
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2卷引用:辽宁省沈阳市2023-2024学年高三上学期教学质量监测(一)数学试题
8 . 已知椭圆
上有不同两点
,
,
,则( )
![](/uploads/image/squformula/b747db7eaf469c6d1607e4b0d028299f.png)
![](/uploads/image/squformula/12a3efb79f35db8448f3391252ab7d4e.png)
![](/uploads/image/squformula/8df332f01628130c084fd46aaca0a4b7.png)
![](/uploads/image/squformula/14436636ec6a7aec09cb63cecf6e970d.png)
a.若![]() ![]() ![]() |
b.![]() ![]() ![]() |
c.若![]() ![]() |
d.![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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解答题-证明题
|
较难(0.4)
|
9 . 已知有
个连续正整数元素的有限集合
(
,
),记有序数对
,若对任意
,
,
,
且
,a同时满足下列条件,则称
为
元完备数对.
条件①:
;
条件②:
.
(1)试判断是否存在3元完备数对和4元完备数对,并说明理由;
(2)试证明不存在8元完备数对.
![](/uploads/image/squformula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](/uploads/image/squformula/244a73e2cab2b626e12058164680d7cd.png)
![](/uploads/image/squformula/6526915197667b48dc2e6c1ff413bcf1.png)
![](/uploads/image/squformula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](/uploads/image/squformula/ac4a8ca987823fe459fafc1c4fd057d6.png)
![](/uploads/image/squformula/2c05b9832b09731a574d4a4adf7448de.png)
![](/uploads/image/squformula/aa9458be5eac5e4b7fbd28850e43d96f.png)
![](/uploads/image/squformula/50a272adba0f1120109824440f0e252c.png)
![](/uploads/image/squformula/ba54a91d651db38d3a13a461252223e0.png)
![](/uploads/image/squformula/a1a205f096c854a2f7cd71255056f9f7.png)
![](/uploads/image/squformula/5963abe8f421bd99a2aaa94831a951e9.png)
![](/uploads/image/squformula/294f5ba74cdf695fc9a8a8e52f421328.png)
条件①:
![](/uploads/image/squformula/9169084fc046cdf9b9831f4030f58217.png)
条件②:
![](/uploads/image/squformula/f34affbf06b09098b13a5b89c0989fb8.png)
(1)试判断是否存在3元完备数对和4元完备数对,并说明理由;
(2)试证明不存在8元完备数对.
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|
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|
名校
解题方法
10 . 已知直线
方程为
,点
,点
到点
的距离与到直线
的距离之比为
,
.
(1)求点
的轨迹
的方程(用
表示);
(2)若斜率为
的动直线
与(1)中轨迹
交于点
,
,其中
,
.点
(
)在轨迹
上,且直线
、
与
轴分别交于
、
两点,若恒有
,求
的值.
![](/uploads/image/squformula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](/uploads/image/squformula/54e756c89b600e37dfb36bb22ef28eb6.png)
![](/uploads/image/squformula/24550b13dbecf7d86c7054250e987274.png)
![](/uploads/image/squformula/ac047e91852b91af639feec23a9598b2.png)
![](/uploads/image/squformula/a0ed1ec316bc54c37c4286c208f55667.png)
![](/uploads/image/squformula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](/uploads/image/squformula/071a7e733d466949ac935b4b8ee8d183.png)
![](/uploads/image/squformula/3e4cc00c283519973f7f8e1274b5c733.png)
(1)求点
![](/uploads/image/squformula/ac047e91852b91af639feec23a9598b2.png)
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
![](/uploads/image/squformula/071a7e733d466949ac935b4b8ee8d183.png)
(2)若斜率为
![](/uploads/image/squformula/274a9dc37509f01c2606fb3086a46f4f.png)
![](/uploads/image/squformula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
![](/uploads/image/squformula/12a3efb79f35db8448f3391252ab7d4e.png)
![](/uploads/image/squformula/8df332f01628130c084fd46aaca0a4b7.png)
![](/uploads/image/squformula/6270bb08b90f72d5671ab8225f356c43.png)
![](/uploads/image/squformula/c2fe3251e054fe97089806ba7033f802.png)
![](/uploads/image/squformula/891fe97a26ca688e22e5d704432f764b.png)
![](/uploads/image/squformula/0b170470d02c85c1be9a3faff5eca0de.png)
![](/uploads/image/squformula/c5db41a1f31d6baee7c69990811edb9f.png)
![](/uploads/image/squformula/bd33764ff4efddfe11a98a609753715c.png)
![](/uploads/image/squformula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](/uploads/image/squformula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](/uploads/image/squformula/8455657dde27aabe6adb7b188e031c11.png)
![](/uploads/image/squformula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](/uploads/image/squformula/374e2198b495b86b0f8308d28035a3db.png)
![](/uploads/image/squformula/071a7e733d466949ac935b4b8ee8d183.png)
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