解题方法
1 . 已知曲线
,圆
,若A,B分别是M,N上的动点,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8afba75dac7dd121de3a5d76393be3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b5123a937059b7dda73ca86b054f77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
A.2 | B.![]() | C.3 | D.![]() |
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2 . 已知
的两个顶点
,
,点G为
的重心,边
上的两条中线的长度之和为6,记点G的轨迹为曲线E.
(1)求曲线E的方程;
(2)若点P是曲线E上的任意一点,
,
,
,
,直线PC,PD与x轴分别交于点M,N.
①求
的最大值;
②判断
是否为定值.若为定值,求出该定值;若不为定值,求出它的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8dfd0ebf16476994cf04dd0f7fafca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13683e2ecf2164a0adbfdb9923d210a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8dfd0ebf16476994cf04dd0f7fafca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6bf421591c540d317587bdac885e9c.png)
(1)求曲线E的方程;
(2)若点P是曲线E上的任意一点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dbc9361f0be545e55976a052e95e960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a375e47ac52f067ac1f7b3f73dbc41ee.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
②判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9467e420cfaea81eb1e7245e3f14c503.png)
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3 . 在平面直角坐标系xOy中,点A,B的坐标分别为
和
,
的周长为6,记顶点M的轨迹为曲线C.
(1)求C的方程;
(2)已知点E,F,P,Q在C上,且直线EF与PQ相交于点A,记EF,PQ的斜率分别为
,
.
(ⅰ)设EF的中点为G,PQ的中点为H,证明:存在唯一常数
,使得当
时,
;
(ⅱ)若
,当
最大时,求四边形EPFQ的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953bfeb398bab2b2ba61b3e6bf0a22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
(1)求C的方程;
(2)已知点E,F,P,Q在C上,且直线EF与PQ相交于点A,记EF,PQ的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(ⅰ)设EF的中点为G,PQ的中点为H,证明:存在唯一常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f132407bf1cc9d1f460d50f1b0547993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b3fa41635da8da11d6c04287ff7513.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129fa211eb0cfb3968d38c3c90249842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7560c67fac3a45cf25ec33aa3ca52519.png)
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解题方法
4 . 已知椭圆的焦点分别是,
,点
在椭圆上,且
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4aafea08192eb812a06147bdb7e8dbd.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/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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5 . 己知圆
,动圆
与圆
相内切,且经过定点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd05f98ba823ac788d3c228d6900191d.png)
(1)求动圆圆心
的轨迹方程;
(2)若直线
与(1)中轨迹交于不同的两点
,记
外接圆的圆心为
(
为坐标原点),平面上是否存在两定点
,使得
为定值,若存在,求出定点坐标和定值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4957438e7f49ced0368ec80649c01ec8.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/bd05f98ba823ac788d3c228d6900191d.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4147f37263dc5cdebcf9d53b758977dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.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/5aa69fd8445d01c98634c2e885b47d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea54c2ea0a0c788a4d85f8d687c45966.png)
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名校
解题方法
6 . 已知复数
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd2f6943430457cb1635515400ce8fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47cdd00c45161e2cdd585a4308b876a.png)
A.![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
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解题方法
7 . 已知复数
,其中
为虚数单位,若
满足
,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db31fcead8e3aff98a0d7712bff575f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314a6d5d5929725092b57b409f97775f.png)
A.![]() ![]() |
B.![]() ![]() |
C.存在两个![]() ![]() |
D.存在两个![]() ![]() |
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名校
解题方法
8 . 已知曲线
,曲线
,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8afba75dac7dd121de3a5d76393be3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c629a4f2909d5a49f1e92b50771a6be6.png)
A.![]() ![]() |
B.若![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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9 . 已知圆
内切于圆
,圆
内切于圆
,则动圆
的圆心的轨迹方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef3bb3154d6b2cecdfe27e03d7a16eb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f5c0404bf281e3c4bfa7c8a6e803cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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10 . 已知圆
,动圆P与圆M内切,且经过定点
.设圆心P的轨迹为曲线
.
(1)求曲线
的轨迹方程;
(2)若
,过点
的直线l与曲线Γ交于M,N两点,连接
分别交y轴于P、Q.试探究
是否为定值?若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88584870885ec28a89f46ca33d8237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e761231888b3eefd1333a499376c9a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d65f0f909b11f0337f3c62842fa742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceadd21e8eb0f48c059a5947f5698378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d42cb68c5c877a455ba7ac0a6b6a651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f34e3ec3ed9e2ac78f9603e24d9648c.png)
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