1 . 在平面直角坐标系
中,动点
(
)与定点
的距离和
到直线
:
的距离之比是常数
.
(1)求动点
的轨迹方程;
(2)记动点
的轨迹为曲线
,过点
的直线
与曲线
交于
两点,直线
与曲线
的另一个交点为
.
(i)求
的值;
(ii)记
面积为
,
面积为
,
面积为
,试问
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/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63309dbc3612815f6dbdee23d9a10adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d599059e6b2c918ab15ee22611b6962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)记动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25fe3ff55350310998d3d4f0048b45a.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53095716c043abb9dd391b3f6e17830.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7783506c9069a5b3c88597a9c8b2f9e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307569acb68c533e026a1f09c6328833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddfea610328ce7f943de71550c743e1.png)
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2024-05-27更新
|
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2卷引用:浙江省绍兴市上虞区2023-2024学年高三下学期适应性教学质量调测数学试卷
名校
解题方法
2 . 孔明锁是中国古代传统益智游戏.左下图即是一个孔明锁.其形状可视为右下图所示的一个几何体:如图,三个轴线相互垂直的长方体的公共部分为一个棱长为1的立方体
,且
,
,
,
,
为其表面上的一个动点,球
为能够使该几何体在其内能够自由转动的最小球体.其中
为球
上的一个动点,以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8cbe156c9bcb80aced48c7568cb3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6153a5d3688dc58103107806dd6c5a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6257d6e4abee4dffd6756d24bca14329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea13389401b703bb45eae76b725cb8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() ![]() |
B.若![]() ![]() ![]() |
C.![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
3 . 已知点
是边长为1的正方体
表面上的动点,若直线
与平面
所成的角大小为
,则点
的轨迹长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 平面内到两定点距离之积为常数的点的轨迹称为卡西尼卵形线,它是1675年卡西尼在研究土星及其卫星的远行规律时发现的.在平面直角坐标系
中,设
到
与
两点的距离之积为2的点的轨迹为曲线
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() |
B.曲线关于原点对称 |
C.曲线围成的面积不大于7 |
D.曲线C上任意两点之间的距离不大于3 |
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名校
解题方法
5 . 如图所示,在棱长为
的正方体
中,则下列命题中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/27/4b319eaa-72ad-49e6-86fb-aa8a9c78bb84.png?resizew=143)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/27/4b319eaa-72ad-49e6-86fb-aa8a9c78bb84.png?resizew=143)
A.若点![]() ![]() ![]() ![]() ![]() |
B.若点![]() ![]() ![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() ![]() |
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2023-02-23更新
|
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3卷引用:浙江省绍兴市诸暨市2022-2023学年高二上学期期末数学试题
6 . 已知
乃是椭圆
的两焦点,
为椭圆上任一点,从
引
外角平分线的垂线,垂足为
,则点
的轨迹方程为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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2022-11-13更新
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1051次组卷
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4卷引用:浙江省绍兴市鲁迅中学2022-2023学年高二普通班上学期期末模拟数学试题
名校
7 . 如图, 二面角
的平面角的大小为
为半平面
内的两个点,
为半平面
内一点, 且
, 若直线
与平面
所成角为
为
的中点, 则线段
长度的最大值是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/69d98e46-6d40-4f1b-8058-5cf008b72771.png?resizew=255)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d9a481d77167a402b59872b538b1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e90d9510b7d495bb79e279abc896d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a769a2ac6ccecc55a9cb48bf6cc4b30c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ac9946fad8b17a7cca85f5027c834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/69d98e46-6d40-4f1b-8058-5cf008b72771.png?resizew=255)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-06-27更新
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3卷引用:浙江省绍兴市第一中学2022-2023学年高二下学期学考模拟数学试题
8 . 已知直线l1:y=k1x和l2:y=k2x与抛物线y2=2px(p>0)分别相交于A,B两点(异于原点O)与直线l:y=2x+p分别相交于P,Q两点,且
.
![](https://img.xkw.com/dksih/QBM/2022/6/8/2996948554473472/2998214561636352/STEM/e63a0709-03a7-4f7e-ae37-2a2dc9d9f3a9.png?resizew=130)
(1)求线段AB的中点M的轨迹方程;
(2)求△POQ面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985a294d39f2a106aa474462ec15dbfb.png)
![](https://img.xkw.com/dksih/QBM/2022/6/8/2996948554473472/2998214561636352/STEM/e63a0709-03a7-4f7e-ae37-2a2dc9d9f3a9.png?resizew=130)
(1)求线段AB的中点M的轨迹方程;
(2)求△POQ面积的最小值.
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2022-06-10更新
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7卷引用:浙江省绍兴市嵊州市2022届高三下学期5月适应性考试数学试题
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9 . 如图,四边形
为平行四边形,
,M,N分别为
的中点,分别将
和
沿
和
折起,点A和点C折起后分别记为
,得到如图几何体
,则
两点间的距离最小值为( )
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975762628812800/2975843725500416/STEM/2eaf9f75-1287-4c0a-af5f-bfef54a813c0.png?resizew=361)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45cdd7c27b5a813b52683cea8a30a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f9fba8a4098c1a0515286eb8d616dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1275768bdac801185ef152290a85ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3467d276bb0f60b45cf34797c7cbe6ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bdb4c4b306e7e11989f54957ea43020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3467d276bb0f60b45cf34797c7cbe6ae.png)
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975762628812800/2975843725500416/STEM/2eaf9f75-1287-4c0a-af5f-bfef54a813c0.png?resizew=361)
A.![]() | B.![]() | C.![]() | D.1 |
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10 . 已知点集
,当
取遍任何实数时,
所扫过的平面区域面积是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9226bb51586313a1ce3770613c325bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-08-24更新
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