1 . 已知点M为椭圆
上任意一点,AB是圆
的一条直径,则
的最大值与最小值的和是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc3985c11ee609d32d6001b6ef237ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de90c03f944e3c277a2cf1ce94f1713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6356488b921e900ad8f0448d20e918e6.png)
A.20 | B.![]() | C.40 | D.![]() |
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2 . 已知O为坐标原点,
,A是
上的动点,连接OA,线段OA交
于点B,过A作x轴的垂线交x轴于点C,过B作AC的垂线交AC于点D,则点D的轨迹方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222a92d9654516761388ed7ce245acdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd73875650e1538c4c61d5e16d3db29.png)
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3卷引用:云南省师范大学附属中学2022届高三高考适应性月考卷(五)数学(理)试题
云南省师范大学附属中学2022届高三高考适应性月考卷(五)数学(理)试题云南省师范大学附属中学2022届高三高考适应性月考卷(五)数学(文)试题(已下线)重难点突破05 求曲线的轨迹方程(十大题型)-2
3 . 双曲线
的一个焦点坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9797634a42031284177e5a6fd5959e39.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:云南省十五所名校2022届高三11月联考数学(理)试题
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解题方法
4 . 已知平面内的两个定点
,
,
,平面内的动点
满足
.记
的轨迹为曲线
.
(1)请建立适当的平面直角坐标系,求
的方程;
(2)过
作直线
交曲线E于A,B两点,
为坐标原点,求
面积的最大值.
![](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/9efbe4a54a27dc48e3f52d6249bd1681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eed5b1b5a80e66f5a6cd08be019376c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)请建立适当的平面直角坐标系,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
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5 . 设点
是函数
的一点,则点
到直线
距离的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89576f3721a6c09912186b990733cd87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7053364523e655abed4a0c887fae69.png)
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解题方法
6 . 已知椭圆
:
的离心率为
,且点
为椭圆
上一点.
(1)求椭圆
的方程.
(2)已知
,直线
:
交椭圆
于A,B两点,证明:直线PA斜率与直线PB斜率之积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9fef6303da730c2ced7f3fbd5e2103d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc422fb174b7424f0b3b297c72aa610d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b640d61e4d350824c645279f9da151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4cd13b1f570f617c7a409b08555079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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1169次组卷
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6卷引用:云南省十五所名校2022届高三11月联考数学(理)试题
名校
解题方法
7 . 若抛物线
的交点为F,过F作直线l与抛物线
交于A,B两点,分别以线段AF,BF为直径作圆
和圆
.
(1)证明:圆
和圆
均与y轴相切;
(2)设圆
与y轴相切于点D,圆
与y相切于点E,求
的值,并求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1354240a807d0da2b51a19e055140165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)证明:圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设圆
![](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/f6c19410c7abeae002ca97cfad4c791f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
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2卷引用:云南省昆明市第一中学2022届高三上学期第四期联考数学(文)试题
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8 . 已知
,
分别为双曲线
的左右焦点,过
作一条直线l与双曲线的右支交于P,Q两点,若
,则
的周长为( )
![](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/1892b7c3cd7bea116f532f66fba44662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d10c567c0419ae04df94f2ccf48992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f744ab198210340a54adb2ae4a6b9b.png)
A.8 | B.10 | C.12 | D.14 |
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7卷引用:云南省昆明市第一中学2022届高三上学期第四期联考数学(文)试题
云南省昆明市第一中学2022届高三上学期第四期联考数学(文)试题云南省昆明市第一中学2022届高三上学期第四期联考数学(理)试题云南省弥勒市第一中学2021-2022学年高二上学期第四次月考数学试题河南省安阳市安东新区第一高级中学2021-2022学年高二上学期12月考试数学试题(已下线)专题2.2 模拟卷(2)-2022年高考数学大数据精选模拟卷(新高考地区专用)(已下线)2.6.1 双曲线的标准方程(2)3.2.1 双曲线的标准方程(同步练习基础版)
名校
解题方法
9 . 已知三棱锥
中,平面
平面
,
,
,点C到点A,B的距离之和为10,设直线PC与平面ABC所成的角为
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72dfe98fd44fa179acc3623bfcc30cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
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2卷引用:云南省昆明市第一中学2022届高三上学期第四期联考数学(文)试题
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解题方法
10 . 已知椭圆
的短轴长为
,离心率为
.
(1)求椭圆
的方程;
(2)若直线
与椭圆
相交于
,
两点(
,
不是左右顶点),且以
为直径的圆过椭圆
的左顶点
,求证:直线
过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
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