1 . 圆锥曲线具有丰富的光学性质,在人教版A版选择性必修第一册的阅读与思考中提到了椭圆的光学性质:从椭圆的一个焦点发出的光线,经过椭圆反射后,反射光线交于椭圆的另一个焦点上,(如图(1)).如图(2),已知
为椭圆
的左焦点,
为坐标原点,直线
为椭圆
的任一条切线,
为
在
上的射影,则点
的轨迹是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/5c9ce68b-3315-4430-b2a6-0635eacad0ba.png?resizew=312)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/5c9ce68b-3315-4430-b2a6-0635eacad0ba.png?resizew=312)
A.圆 | B.椭圆 | C.双曲性 | D.抛物线 |
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2 . 高为3,长宽为
的长方体
中,以
为球心的球
两两相切,过
点作球
的切线
交球
于点
在长方体外部,则点
的轨迹长度是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643bd09a49be5515e3616a6acc3ee6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fd4dfee3258dc4e386330bac4ef0f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dacb04fa29178c0af4353e4369a7e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dacb04fa29178c0af4353e4369a7e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71583df127d58ed2b9ae421aadae7ec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 已知长方体,其中
,
,
为底面
上的动点,
于
且
,设
与平面
所成的角为
,则
的最大值为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 2022年卡塔尔世界杯会徽(如图)正视图近似于伯努利双纽线,定义在平面直角坐标系xOy中(O为坐标原点),把到定点
和
距离之积等于
的点的轨迹称为双纽线,记为Γ,已知
为双纽线Γ上任意一点,有下列命题:
①双纽线Γ的方程为
;
②
面积最大值为
;
③
;
④
的最大值为
.
其中所有正确命题的序号是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/d00e368b-8731-48cf-9176-ee3cd015758a.png?resizew=117)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6dc791ae552024ea0df7905bf190f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace7c9e3da8613175ca07c54c116127a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd789f3b1f753a6608e4ca80feb275b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
①双纽线Γ的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d5c1027563eccb6347cd64aaf8a068.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5897d99cc9414875f512f8cb3f5c5f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e3077992897631e1123d481c7a230a.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f625aa2ab29879c1df77417e9c1cf71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8bfae3435fcf141dcdd83e1ad4f1b6d.png)
其中所有正确命题的序号是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/d00e368b-8731-48cf-9176-ee3cd015758a.png?resizew=117)
A.①② | B.①②③ |
C.②③④ | D.①②③④ |
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解题方法
5 . 已知双曲线
与直线
有唯一的公共点
,过点
且与
垂直的直线分别交
轴、
轴于
两点,当点
运动时,点
的轨迹方程是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6d37b4c6d03441fd2966ee1e8af41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de3eca71de86a01a83e25af71c143b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cda5a4c295b2817b357e641564ef186.png)
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名校
6 . 已知双曲线
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b30352c43707c4e54b94ce5b61f2e6.png)
A.双曲线C的顶点到其渐近线的距离为2 |
B.若F为C的左焦点,点P在C上,则满足![]() ![]() |
C.若A,B在C上,线段AB的中点为![]() ![]() |
D.若P为双曲线上任意一点,则点P到点![]() ![]() |
您最近一年使用:0次
2022-02-17更新
|
376次组卷
|
2卷引用:浙江省宁波市北仑中学2021-2022学年高二下学期期初考试数学试题
7 . 设
,定义区间
、
、
、
的长度均为
.在三棱锥
中,
,
,
,
,则
长的取值区间的长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8845c0d06613fabb0358d5392cca38b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b639b8a34097101c0a4767ea34c13884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152e7be0c0054be3a8d537ef39d35da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650c6c818df102a83ce5159e3208d01a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
A.2 | B.![]() | C.3 | D.![]() |
您最近一年使用:0次
名校
8 . 如图,设圆
,现将半圆
所在平面沿
轴折起(坐标轴不动),使之与半平面
成
的二面角,若点
为半圆
上的动点,则点
在半圆
所在平面上的射影的轨迹方程为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176385d91d5e29324fce4a932eff6a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a74b68d468975a4b599f14764014308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176385d91d5e29324fce4a932eff6a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a74b68d468975a4b599f14764014308.png)
![](https://img.xkw.com/dksih/QBM/2021/9/1/2798795293638656/2799244263653376/STEM/9b34435b-8324-4d38-a1fb-da427cced1d3.png?resizew=221)
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名校
9 . 如图,已知平面
,
,A、B是直线l上的两点,C、D是平面
内的两点,且
,
,
,
,
.P是平面
上的一动点,且直线PD,PC与平面
所成角相等,则二面角
的余弦值的最小值是( )
![](https://img.xkw.com/dksih/QBM/2022/10/8/3083512504377344/3083829352857600/STEM/f9cbdbcd5aa34d858372e340ab7b9b08.png?resizew=345)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5986f2991d45fbf3578f08f27d9fd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b707f5ee4fbb2e637c65fbc6d8ed03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e498078756c976d87931c17185a0ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c875d12a4ee3a9b6656bdfe4919ad18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cd495dbd7296b0092fa3e1ef77477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715cc9ea5e7d80930284ffb117142770.png)
![](https://img.xkw.com/dksih/QBM/2022/10/8/3083512504377344/3083829352857600/STEM/f9cbdbcd5aa34d858372e340ab7b9b08.png?resizew=345)
A.![]() | B.![]() | C.![]() | D.1 |
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2022-10-09更新
|
1933次组卷
|
10卷引用:浙江省金华市兰溪市第三中学2020届高三下学期寒假返校考试数学试题
浙江省金华市兰溪市第三中学2020届高三下学期寒假返校考试数学试题【全国百强校】浙江省余姚中学2018届高三选考科目模拟卷(二)数学试题1浙江省余姚中学2018届高三选考科目模拟考试(一)数学试题2018届浙江省宁波市余姚中学高三下学期6月高考适应性考试数学试题2017届江西鹰潭一中高三理上学期月考五数学试卷江西省吉安市省重点中学2020-2021学年高二年级(10月)联合考试文科数学试题(已下线)专题1 阿波罗尼斯圆及其应用 微点5 阿波罗尼斯球(已下线)专题27 直线与圆的综合应用-2(已下线)重难点突破03 直线与圆的综合应用(七大题型)(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点8 空间范围与最值问题综合训练
10 . 如图,已知正方体
的棱长为2,P是平面
内的动点,Q是
上一点且
,若点P到
的距离与P,Q距离的平方差等于4,则点P的轨迹为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/cb3507ea-c29b-4843-88d9-794cfd5321f6.png?resizew=141)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ecec69ebfb4d63d11e4859451b6523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/cb3507ea-c29b-4843-88d9-794cfd5321f6.png?resizew=141)
A.直线 | B.抛物线 | C.椭圆 | D.双曲线 |
您最近一年使用:0次