名校
解题方法
1 . 已知抛物线
上的点
到其焦点的距离为
.
(1)求
和
的值;
(2)若直线
交抛物线
于
、
两点,线段
的垂直平分线交抛物线
于
、
两点,求证:
、
、
、
四点共圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365c238724dea5c24c3e326678c9ed54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ce81c2674a74d4704f9ce387ef954f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2022-09-01更新
|
1712次组卷
|
11卷引用:新疆维吾尔自治区乌鲁木齐市第十二中学2024届高三上学期9月月考数学(文)试题
新疆维吾尔自治区乌鲁木齐市第十二中学2024届高三上学期9月月考数学(文)试题四川省泸州市2021届高三三模数学(文)试题(已下线)第46讲 解析几何中的四点共圆问题-2022年新高考数学二轮专题突破精练2023版 湘教版(2019) 选修第一册 过关斩将 第3章 综合拔高练(已下线)专题7 解决曲线的几何性质的运算(提升版)四川省南充市阆中中学校2022-2023学年高三上学期10月月考数学(文)试题(已下线)考向36 直线与圆锥曲线最全归纳(十六大经典题型)-3(已下线)专题38 圆锥曲线中的圆问题-2(已下线)第五篇 向量与几何 专题10 圆锥曲线中的四点共圆问题 微点2 圆锥曲线中的四点共圆问题(二)(已下线)重难点突破15 圆锥曲线中的圆问题(四大题型)(已下线)专题03 圆锥曲线题型全归纳(九大考点)-【寒假自学课】2024年高二数学寒假提升学与练(人教A版2019)
名校
2 . 如图,在四棱锥
中,已知四边形
是梯形,
,
是正三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/683b6788-5b7e-4317-b643-bf3b4dbf07ac.png?resizew=179)
(1)求证:
;
(2)当四棱锥
体积最大时,二面角
的大小为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f2693cdb3751a8fd3a5d6f597dcfbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e68c3b4e4aff8c6b7f8b6189e3985f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/683b6788-5b7e-4317-b643-bf3b4dbf07ac.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3723525244e12b59101e1c0b5fb912ca.png)
(2)当四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8860d255b9c6cec4c062d73720aa8a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2930e3d72846688f8389ab8cf178e062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b8b77522dfc890b99f0a86a690de94.png)
您最近一年使用:0次
2022-10-23更新
|
248次组卷
|
3卷引用:新疆生产建设兵团第三师图木舒克市第二中学2023届高三上学期月考数学(理)试题
名校
解题方法
3 . 如图,在直三棱柱
中,
,E为
的中点,F为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/11/2/3101160789360640/3102278856802304/STEM/67755079c1a64c7eab5dc1c2b5487aa3.png?resizew=212)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)若
,求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2022/11/2/3101160789360640/3102278856802304/STEM/67755079c1a64c7eab5dc1c2b5487aa3.png?resizew=212)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96a6b20a35af7755e5d90789ea862da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2022-11-04更新
|
617次组卷
|
2卷引用:新疆维吾尔自治区乌鲁木齐市第101中学2023届高三上学期12月月考理科数学试题
名校
解题方法
4 . 如图,在四棱锥
中,
平面
,
,底面ABCD是边长为4的菱形,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee296a7d9fba487f1485c61580196f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/29/795f868f-ed75-4857-8a92-b366d4066bc5.png?resizew=143)
(1)求证:
;
(2)求平面PAC与平面PCD夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19f0fcacac715a1200770516d1e4a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee296a7d9fba487f1485c61580196f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/29/795f868f-ed75-4857-8a92-b366d4066bc5.png?resizew=143)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(2)求平面PAC与平面PCD夹角的余弦值.
您最近一年使用:0次
2023-01-13更新
|
201次组卷
|
2卷引用:新疆昌吉州行知学校2023届高三下学期第一次月考数学(理)试题
名校
5 . 如图所示,三棱台
的体积为7,其上、下底面均为正三角形,平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2c649fe991df124faaef9dc8876c22.png)
且
,棱
与
的中点分别为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/1f91547d-a6a0-4d6c-857d-18dd1a0f824f.png?resizew=229)
(1)证明:
平面
;
(2)求直线
到平面
的距离;
(3)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7d82423b6f211a7ac51a850b55e73a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2c649fe991df124faaef9dc8876c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604f9bbc0657e96ecf3f2e6f47a3c3f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ddfedec4aab9d2000de0eb6520a936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/1f91547d-a6a0-4d6c-857d-18dd1a0f824f.png?resizew=229)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
您最近一年使用:0次
2022-10-14更新
|
684次组卷
|
6卷引用:新疆石河子第一中学2022-2023学年高二上学期10月月考数学(理)试题
新疆石河子第一中学2022-2023学年高二上学期10月月考数学(理)试题皖豫名校联盟2022-2023学年高二上学期阶段性测试(一)数学试题河南省安阳市2022-2023学年高二上学期阶段性测试(一)数学试题河南省部分学校联考2022-2023学年高二上学期阶段性测试(一)数学试卷(A卷)安徽省合肥市肥西县宏图中学2022-2023学年高二上学期第一次月考数学试题(已下线)期中押题预测卷01(考试范围:选择性必修第一册)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教A版2019)
名校
6 . 如图,在四棱锥
中,平面
平面
,四边形
是边长为2的菱形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/17/7a27efab-0905-47af-8083-aef2eba0e679.png?resizew=163)
(1)求证:
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/17/7a27efab-0905-47af-8083-aef2eba0e679.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccd5c41c921836b50f8e18abfdc5df3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec435aa1401dbce7863b531bf2f3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
2022-07-12更新
|
1235次组卷
|
2卷引用:新疆维吾尔自治区乌鲁木齐市第101中学2022-2023学年高二上学期12月月考数学试题
名校
解题方法
7 . 在平面直角坐标系
中,已知点
在抛物线
上,圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696194073d11052786104e11178adf2e.png)
(1)若
,
为圆
上的动点,求线段
长度的最小值;
(2)若点
的纵坐标为4,过
的直线
与圆
相切,分别交抛物线
于
(异于点
),求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8a3bffe545af2299cf999d44767206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696194073d11052786104e11178adf2e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)若点
![](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/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-12-11更新
|
545次组卷
|
3卷引用:新疆维吾尔自治区乌鲁木齐市第四十中学2023届高三下学期4月月考理科数学试题
名校
8 . 如图,在多面体
中,四边形
是矩形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e3a8f4ea4c49537514dd22064100f9.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b4146b39-5172-455e-95ca-7865cb927a8b.png?resizew=188)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e3a8f4ea4c49537514dd22064100f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307492a5106b38351e52cd4fff8b1ec8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b4146b39-5172-455e-95ca-7865cb927a8b.png?resizew=188)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e49a850dd76dc1162ff2eda8791b772.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
您最近一年使用:0次
2023-01-16更新
|
282次组卷
|
2卷引用:新疆乌鲁木齐市第六十一中学2024届高三上学期12月月考数学试题
10-11高三·江西南昌·阶段练习
名校
9 . 如图所示,在矩形ABCD中,
,
,E是CD的中点,O为AE的中点,以AE为折痕将
向上折起,使D点折到P点,且
.
面ABCE;
(2)求AC与面PAB所成角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89cd4aa28b07f2ff7cf0e1b66e67f6c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
(2)求AC与面PAB所成角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2022-08-15更新
|
1648次组卷
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13卷引用:新疆巴音郭楞蒙古自治州第二中学2021届高三第六次月考数学(理)试题
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10 . 如图,在四棱锥P-ABCD中,底面ABCD是正方形,侧棱PD⊥底面ABCD,PD=DC,E是PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/5f500796-8bf1-4115-87cc-f983bfd11f2d.png?resizew=235)
(1)求证:
平面EBD
(2)求PB与平面EBD所成的角的正弦值
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/5f500796-8bf1-4115-87cc-f983bfd11f2d.png?resizew=235)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
(2)求PB与平面EBD所成的角的正弦值
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