解题方法
1 . 已知正方体
的棱长为
分别是棱
的中点,
是棱
上的动点(包括端点),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2612d8c87010adfe87728a591b63e3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88eefaa74efafcea0c9f623190c3ddd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
A.![]() |
B.正方体的外接球的球心可能在平面![]() |
C.若直线![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() ![]() |
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解题方法
2 . 在平面直角坐标系
中,点
是拋物线
的焦点,
到
的准线
的距离为2,点
是
上的动点,过点
且与
相切的直线
与
轴交于点
是准线
上的一点,且
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d55d55d7c4c79495f9e1ea44b278f93a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c638fb895acd987140d0ca6bef097499.png)
A.![]() |
B.当点![]() ![]() |
C.设![]() ![]() ![]() |
D.![]() |
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3 . 如图,已知椭圆
的左、右顶点分别是
,上顶点为
,在椭圆上任取一点
(非长轴端点),连接
交直线
于点
,连接
交
于点
(
是坐标原点),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d324b8cc99df14a6418e7d0f7b7d7436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb85d28f8bdeedad66fd7ec2a561455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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解题方法
4 . 已知
分别为椭圆
的左、右焦点,P为椭圆上任意一点(不在x轴上),
外接圆的半径为R,
内切圆的圆心为I,半径为r,直线PI交x轴于点M,G为
的重心,O为坐标原点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef0f8bf9bb8e9b7a4d48a9abba7b1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
A.r为定值 | B.![]() |
C.![]() ![]() | D.直线IG的倾斜角不变 |
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5 . 已知斜率为
的直线交抛物线
于
、
两点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e3dcb7f9fa27f3d07d18a61d4bb36e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c971815096aafba83743ab5e4c89d78.png)
A.![]() | B.线段![]() |
C.![]() | D.![]() ![]() |
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解题方法
6 . 设椭圆
:
的左、右焦点分别为
、
,
是
上的动点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.椭圆![]() ![]() |
B.![]() |
C.![]() |
D.![]() ![]() |
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7 . 已知抛物线Γ:
,过点
作直线
,直线
与Γ交于A,C两点,A在x轴上方,直线
与Γ交于B,D 两点,D在x轴上方,连接
,若直线
过点
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290a56449ad6dd65aec7525c94273f59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57901924f7747648bcaca87f0bf9915d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d54c40e77fc6b5d018e5d1ab271c450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
A.若直线![]() ![]() ![]() |
B.直线![]() ![]() |
C.直线![]() ![]() ![]() |
D.![]() ![]() ![]() |
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解题方法
8 . 椭圆
的焦点为
,
,上顶点为A,直线
与C的另一个交点为B,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e52aa67b1c6d06d8f4bbb19075a767a.png)
![](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/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a62cd39019b41b4bc2e7df87844868.png)
A.C的焦距为2 | B.C的短轴长为![]() |
C.C的离心率为![]() | D.![]() |
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9 . 如图,在棱长为2的正方体
中,点P是侧面
内的一点,点E是线段
上的一点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
A.当点P是线段![]() ![]() ![]() |
B.当点E为线段![]() ![]() ![]() |
C.点E到直线![]() ![]() |
D.当点E为棱![]() ![]() ![]() |
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解题方法
10 . 已知抛物线
焦点为
,过点
(不与点
重合)的直线交
于
两点,
为坐标原点,直线
分别交
于
两点,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/400abb6d0bb0618dde67160941b8853f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1167767fd847678ef279f3e637f2828.png)
A.![]() | B.直线![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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