1 . 已知
,直线
,
.
(1)证明:到
、
的距离的平方和为定值
的点的轨迹是圆或椭圆;
(2)求到
、
的距离之和为定值
的点的轨迹.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4a45e79f51c7b5a9428f4cf2ab5c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df7b3f985f80216134feed07422c9e1.png)
(1)证明:到
![](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/a6ec1e326713ddcd6dd66a24a809bdb8.png)
(2)求到
![](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/461cc091b28cd0e098b91c4600449e4a.png)
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2022-11-09更新
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2卷引用:2004 年普通高等学校招生考试数学(文)试题(安徽卷)
真题
解题方法
2 . 如图,在四棱锥
中,底面
是边长为1的菱形,
,
底面
,
,
为
的中点.
(Ⅰ)求异面直线AB与MD所成角的大小;
(Ⅱ)求点B到平面OCD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6baf49925a5bcb359b542d45067c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317430d5a2b61d9a2a88b73e7d7ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
(Ⅰ)求异面直线AB与MD所成角的大小;
(Ⅱ)求点B到平面OCD的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/e20085dd-f55b-4e1e-bc28-b27ab2a3b44c.png?resizew=170)
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2019-01-30更新
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2卷引用:2008年普通高等学校招生全国统一考试数学文科(安徽卷)
真题
解题方法
3 . 已知椭圆
经过点
,对称轴为坐标轴,焦点
在
轴上,离心率
.
![](https://img.xkw.com/dksih/QBM/2010/6/8/1569758978654208/1569758983790592/STEM/784698c675a8424886efa0787d2b39f6.png?resizew=249)
(Ⅰ)求椭圆
的方程;
(Ⅱ)求
的角平分线所在直线
的方程;
(Ⅲ)在椭圆
上是否存在关于直线
对称的相异两点?若存在,请找出;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e8f7e3beb2c3bc522d5bde3dd93af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://img.xkw.com/dksih/QBM/2010/6/8/1569758978654208/1569758983790592/STEM/784698c675a8424886efa0787d2b39f6.png?resizew=249)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62180fb2b68724b7b0f4f8337496c12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅲ)在椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2019-01-30更新
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1432次组卷
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4卷引用:2010年普通高等学校招生全国统一考试(安徽卷)数学试题(理科)
2010年普通高等学校招生全国统一考试(安徽卷)数学试题(理科)(已下线)2011-2012学年四川省巴中市四县中高二上学期期末考试文科数学2016届浙江省余姚中学高三上学期期中理科数学试卷(已下线)专题19 圆锥曲线与角平分线定理 微点1 圆锥曲线与角平分线定理
真题
4 . 如图,
分别是椭圆
:
+
=1(![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/391905d6302b4d458d62bf766c885bf1.png)
)的左、右焦点,
是椭圆
的顶点,
是直线
与椭圆
的另一个交点,![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/aaa10b2235634c8fb9d791902520a123.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/a6357bb1befa4687887ce1726984348b.png)
=60°.
(Ⅰ)求椭圆
的离心率;
(Ⅱ)已知△![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/a6357bb1befa4687887ce1726984348b.png)
的面积为40
,求
的值.
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/1025d9dc759b4fa9ab24fb5f644df70b.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/95bb39bfb60341f6ab249349e9d9e0d3.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/62334707b5254f54bdf7075297bed67d.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/b5ff602e30c64bf99db16588b5daa02a.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/391905d6302b4d458d62bf766c885bf1.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/b5e7547395b746f59f3e76f5c5356f16.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/a6357bb1befa4687887ce1726984348b.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/95bb39bfb60341f6ab249349e9d9e0d3.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/0946937d2d8148b9b075957fa021adb4.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/667e455e0b174760a50df884095cbe0e.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/95bb39bfb60341f6ab249349e9d9e0d3.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/aaa10b2235634c8fb9d791902520a123.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/a6357bb1befa4687887ce1726984348b.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/ddbe4f8e8ebd4b0b877056daa0d69216.png)
(Ⅰ)求椭圆
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/95bb39bfb60341f6ab249349e9d9e0d3.png)
(Ⅱ)已知△
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/a6357bb1befa4687887ce1726984348b.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/78138db7055048a4a2c1ed50e4459ee7.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570886955196416/1570886960857088/STEM/90042fbbb05f43f88809d8306656a737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/9cc73f70-f9c8-4574-9802-d89680a1d781.png?resizew=197)
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真题
解题方法
5 . 如图,四棱锥F-ABCD的底面ABCD是菱形,其对角线AC=2,BD=
.AE、CF都与平面ABCD垂直,AE=1,CF=2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/d786093e-0328-40b3-b5b9-881e38728090.png?resizew=144)
(Ⅰ) 求二面角B-AF-D的大小;
(Ⅱ) 求四棱锥E-ABCD与四棱锥F-ABCD公共部分的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/d786093e-0328-40b3-b5b9-881e38728090.png?resizew=144)
(Ⅰ) 求二面角B-AF-D的大小;
(Ⅱ) 求四棱锥E-ABCD与四棱锥F-ABCD公共部分的体积.
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6 . 设椭圆E的方程为
,点O为坐标原点,点A的坐标为
,点B的坐标为
,点M在线段AB上,满足
,直线OM的斜率为
.
(1)求E的离心率e;
(2)设点C的坐标为
,N为线段AC的中点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1f08e04cf0b6a9afea66ce590ba00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad29801f799532ee7dda9658c30e373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca45bff8f7dd6a8cc5843237c072a590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fd7940df8100511c9b98ed85d014a3.png)
(1)求E的离心率e;
(2)设点C的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3120582c4f0b7a6f55a5f95cab654a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f479d987bc7abd828c64f9dc745836ab.png)
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2016-12-03更新
|
2615次组卷
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8卷引用:2015年全国普通高等学校招生统一考试文科数学(安徽卷)
2015年全国普通高等学校招生统一考试文科数学(安徽卷)黑龙江省牡丹江市第一高级中学2018届高三10月月考数学(文)试题智能测评与辅导[文]-椭圆(已下线)专题9.6 直线与圆锥曲线(精练)-2021年高考数学(文)一轮复习学与练2023版 北师大版(2019) 选修第一册 名师精选卷 第六单元 椭圆 A卷2023版 苏教版(2019) 选修第一册 名师精选卷 第六单元 椭圆A卷(已下线)第04讲 圆锥曲线的综合问题(讲)(已下线)专题24 解析几何解答题(文科)-3
真题
解题方法
7 . 设椭圆E的方程为
,点O为坐标原点,点A的坐标为
,点B的坐标为
,点M在线段AB上,满足
,直线OM的斜率为
.
(Ⅰ)求E的离心率e;
(Ⅱ)设点C的坐标为
,N为线段AC的中点,点N关于直线AB的对称点的纵坐标为
,求E的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443a92b0ee19ee3f16db4580c86b3998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72dced07d9ef20de13720b6fe4d357ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ace529fde6b0fbf44305cb73ed309d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fd7940df8100511c9b98ed85d014a3.png)
(Ⅰ)求E的离心率e;
(Ⅱ)设点C的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ea3fd08fcd1bd0105c3ac1cf1c2b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec85f29c0860b57a8f0cf8098c13a97e.png)
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2016-12-03更新
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10卷引用:2015年全国普通高等学校招生统一考试理科数学(安徽卷)
2015年全国普通高等学校招生统一考试理科数学(安徽卷)2015-2016学年江苏省泰州市姜堰区高二上学期期中考试理科数学试卷2015-2016学年江苏省泰州市姜堰区高二上学期期中考试文科数学试卷苏教版高中数学 高三二轮 专题16 圆锥曲线基本问题 测试(已下线)实战演练8.3-2018年高考艺考步步高系列数学智能测评与辅导[理]-椭圆(已下线)专题26 椭圆-十年(2011-2020)高考真题数学分项(已下线)选择性必修第一册综合复习与测试03-2021-2022学年高二数学课后培优练(人教A版2019选择性必修第一册)(已下线)专题26 求动点轨迹方程 微点3 待定系数法求动点的轨迹方程(已下线)专题24 解析几何解答题(理科)-1
真题
名校
8 . 设
,
分别是椭圆
:
的左、右焦点,过点
的直线交椭圆
于
两点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4331e0fcdfd168b17679e97dbf8ec994.png)
(1)若
的周长为16,求
;
(2)若
,求椭圆
的离心率.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac095377b5a2b72d7580bfe33431163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/4331e0fcdfd168b17679e97dbf8ec994.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d622fbe043587560afab936224d80c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d93439559f1be40f46bef7f31ca1e88.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/396b6b8d9d5bdc95a9a5a338fb6394a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2016-12-03更新
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|
34卷引用:2014年全国普通高等学校招生统一考试文科数学(安徽卷)
2014年全国普通高等学校招生统一考试文科数学(安徽卷)【市级联考】安徽省定远重点中学2018-2019学年高二上学期第三次月考数学(理)试题安徽省合肥市肥东县综合高中2022-2023学年高二上学期11月期中考试数学试题(已下线)2018年11月4日 《每日一题》一轮复习(理)-每周一测(已下线)2018年11月4日 《每日一题》一轮复习(文)-每周一测黑龙江省齐齐哈尔市第八中学2019-2020学年高二9月月考数学(理)试题四川省攀枝花市第十五中学2019-2020学年高二上学期第一次月考数学文科试题四川省攀枝花市第十五中学2019-2020学年高二上学期第一次月考数学理科试卷(已下线)专题26 椭圆-十年(2011-2020)高考真题数学分项江苏省南京师范大学附属苏州实验学校2020-2021学年高二上学期教学质量调研(二)数学试题陕西省咸阳市武功县普集高中2020-2021学年高二上学期第三次月考数学(文)试题陕西省西安市长安区第一中学2020-2021学年高二上学期第一次教学质量检测数学(文)试题青海省西宁市普通高中五校2020-2021学年高二上学期期末联考数学(理)试题河北省元氏县第四中学2020-2021学年高二上学期期末数学试题河北省石家庄市第二中学2022届高三上学期开学考试数学试题(已下线)第二课时 课后 3.1.2 第1课时 椭圆的几何性质河北省武强县武强中学2020-2021学年高二上学期第二次月考数学试题苏教版(2019) 选修第一册 突围者 第3章 第一节 课时2 椭圆的几何性质山东省淄博市淄川中学2018-2019学年高二6月月考数学试题(已下线)3.1.2 第1课时 椭圆的简单几何性质(分层练习)-2021-2022学年高二数学教材配套学案+课件+练习(人教A版2019选择性必修第一册)人教A版(2019) 选修第一册 实战演练 第三章 课时练习22 椭圆的简单几何性质甘肃省兰州市第一中学2021-2022学年高二上学期期末考试数学(文)试题黑龙江省齐齐哈尔市实验中学2021-2022学年高二上学期期中数学试题(已下线)专题16 圆锥曲线焦点弦 微点1 圆锥曲线焦点弦三角形周长陕西省西安市临潼区铁路中学2022-2023学年高二上学期第二次月考理科数学试题内蒙古乌兰察布市化德县第一中学2022-2023学年高二上学期期末数学(理)试题内蒙古乌兰察布市化德县第一中学2022-2023学年高二上学期期末考试数学(文)试题上海市向明中学2022-2023学年高二下学期期中数学试题吉林省长春外国语学校2022-2023学年高二上学期11月期中数学试题江苏省江都中学、仪征中学2023-2024学年高二上学期10月联考数学试题(已下线)考点11 圆锥曲线的定义及其应用(椭圆,双曲线,抛物线) 2024届高考数学考点总动员(已下线)BBWYhjsx1108(已下线)专题24 解析几何解答题(文科)-2上海市大同中学2023-2024学年高二下学期期中考试数学试卷
9 . 如图,四棱柱
中,![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/596f01c22a6b4791a2ec63bd661fd429.png)
底面
.四边形
为梯形,
,且
.过
三点的平面记为
,
与
的交点为
.
(1)证明:
为
的中点;
(2)求此四棱柱被平面
所分成上下两部分的体积之比;
(3)若![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/596f01c22a6b4791a2ec63bd661fd429.png)
,
,梯形
的面积为6,求平面
与底面
所成二面角大小.
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/2fc9ffddd0dd414bb43f277be481882c.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/596f01c22a6b4791a2ec63bd661fd429.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/8cadd2a06907476387af1fab080df0d7.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/260bdd891a01497cb1d5186c01a71651.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/260bdd891a01497cb1d5186c01a71651.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/450b8c92f03241108169cf1af53f4089.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/3add4f59a61140d398a6e8961ed10143.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/c39a275a980c48258e0a9f63850249da.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/04bb3358044143c0a7917a9aba6f5516.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/ad148f0a1a884d7fa7a86cdff63c5822.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/04bb3358044143c0a7917a9aba6f5516.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/613a5ceca8174a10b921e31320d10024.png)
(1)证明:
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/613a5ceca8174a10b921e31320d10024.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/ad148f0a1a884d7fa7a86cdff63c5822.png)
(2)求此四棱柱被平面
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/04bb3358044143c0a7917a9aba6f5516.png)
(3)若
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/596f01c22a6b4791a2ec63bd661fd429.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/cdfb0865f83a4b318854af80e2164293.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/e2a8ab04577541d9aa1dc7c2bcb8d83a.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/260bdd891a01497cb1d5186c01a71651.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/04bb3358044143c0a7917a9aba6f5516.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/260bdd891a01497cb1d5186c01a71651.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/9dfed7d9-ea66-4a82-b56c-9c0ba6638f06.png?resizew=191)
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真题
10 . 如图,已知两条抛物线
和
,过原点
的两条直线
和
,
与
分别交于
两点,
与
分别交于
两点.
(1)证明:![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/af7f34a4ecb640aa9912b3b9aae55fc9.png)
(2)过原点
作直线
(异于
,
)与
分别交于
两点.记
与
的面积分别为
与
,求
的值.
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/02a2898938f84725a0d7bd3bacd43823.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/39b49225840c4820bdd8599e51605fe2.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/add7089ad7b447468f1d4337ed5c46b9.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/c805a26f85f149848c004e63af44f92f.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/69eeeb050c114038a2d6354a282ce6a3.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/c805a26f85f149848c004e63af44f92f.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/2dab8d4b482f49a9ad4f94b7319a89be.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/4b102ac493e04fb09667008e90d26250.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/69eeeb050c114038a2d6354a282ce6a3.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/2dab8d4b482f49a9ad4f94b7319a89be.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/66fc5cbf25e048aba7678668907dc251.png)
(1)证明:
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/af7f34a4ecb640aa9912b3b9aae55fc9.png)
(2)过原点
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/add7089ad7b447468f1d4337ed5c46b9.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/39a47fe0602d4fdfa27df6e14b5f8976.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/c805a26f85f149848c004e63af44f92f.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/69eeeb050c114038a2d6354a282ce6a3.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/2dab8d4b482f49a9ad4f94b7319a89be.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/b2cbf7a12cfe470ca5e1ac4772d0e62f.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/1704d0d33971403480ce925b2447660c.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/4651b61762ac4e2b9e9c0aec5c0c2f34.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/7e10fc70d12547a496ccf2090310a39a.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/2e6b2277187c41cab63f71c2dd1a739f.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449569792/STEM/d08f7b7720ba40d7bcbdfb00cf7d364a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/8e386539-87ff-481f-a71a-20a7f461f717.png?resizew=202)
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