名校
1 . 已知椭圆
的离心率为
,
、
分别为椭圆
的左、右顶点,点
满足
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)设直线
经过点
且与
交于不同的两点
、
,试问:在
轴上是否存在点
,使得直线
与直线
的斜率的和为定值?若存在,请求出点
的坐标及定值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026fced6e02fab3a836d0f0280d3f3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879080beb1e55cae2639645cd64c4710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5ead847c543d5b0cba7812278a759a.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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2018-03-14更新
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7卷引用:江西省九江三中2019届高三上学期中理数试题
江西省九江三中2019届高三上学期中理数试题(已下线)河北省衡水中学2019届高三上学期期中考试理科数学试题陕西省西安市长安区第五中学2019届高三上学期期中考试数学(理)试题天津市津南区咸水沽第一中学2020-2021学年高二上学期期中数学试题广东省六校(广州二中,深圳实验,珠海一中,中山纪念,东莞中学,惠州一中)2018届高三下学期第三次联考数学(理)试题广东省珠海一中等六校2018届高三第三次联考数学理试题(已下线)专题24 圆锥曲线中的存在性、探索性问题 微点2 圆锥曲线中的探索性问题
2014高三·全国·专题练习
名校
2 . 已知椭圆
的两个焦点分别为
,
,离心率为
,且过点
.
(
)求椭圆
的标准方程.
(
)
、
、
、
是椭圆
上的四个不同的点,两条都不和
轴垂直的直线
和
分别过点
,
,且这条直线互相垂直,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e501efaf72113fc8ee3d495004fa980.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.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/871dc8a502979244cb0d970ef3233976.png)
您最近一年使用:0次
2017-12-25更新
|
1654次组卷
|
8卷引用:江西省赣州市十四县(市)2017-2018学年高二下学期期中联考数学(文)试题
江西省赣州市十四县(市)2017-2018学年高二下学期期中联考数学(文)试题北京市西城区育才中学2017-2018学年高二上学期期中考试数学(理)试题(已下线)2014年高考数学文复习二轮作业手册新课标·通用版限时集15讲练习卷安徽省六安市第一中学2018届高三下学期第三次模拟考试数学(文)试题(已下线)2018年11月25日 《每日一题》理数人教选修2-1-每周一测(已下线)2018年11月25日 《每日一题》文数人教选修1-1-每周一测新疆实验中学2018-2019学年高二下学期开学检测数学试题四川省内江市威远中学2020-2021学年高二下学期期中考试数学(文)试题
3 . 椭圆
与直线
相交于
、
两点,且
,其中
为坐标原点.
(1)求
的值;
(2)若椭圆的离心率
满足
,求椭圆长轴长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0dce10bf671cc2ebc67aa7fd568a9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45900deae0489e87fe448948e8091c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0687b9f2612100122ef9e2f4a85bce.png)
(2)若椭圆的离心率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c57a35ecae403fe3d51f8baf017319a.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
过点
,离心率为
.
(1)求椭圆的标准方程;
(2)过椭圆的上顶点作直线
交抛物线
于
、
两点,
为原点.
①求证:
;
②设
、
分别与椭圆相交于
、
两点,过原点
作直线
的垂线
,垂足为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c9bebea391a1f9956dfcca98d9d1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c778b2d3185e80c9c00cd6fe156d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆的标准方程;
(2)过椭圆的上顶点作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.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/1dde8112e8eb968fd042418dd632759e.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4cd68cc82e90a5e2049a7ea3171b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a31666076b1d37cd2f99afa950da5ab.png)
您最近一年使用:0次
2017-11-29更新
|
1317次组卷
|
4卷引用:江西省南昌市第二中学2017-2018学年高二上学期期中考数学(文)试题
10-11高三上·广东深圳·期中
5 . 已知椭圆的中心在原点,焦点在
轴上,长轴长是短轴长的2倍且经过点
,平行于
的直线
在
轴上的截距为
,
交椭圆于
两个不同点.
(1)求椭圆的标准方程以及
的取值范围;
(2)求证直线
与
轴始终围成一个等腰三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87484a879f450ab097f720fb2a0f4a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求椭圆的标准方程以及
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求证直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03df57efff473b3cfeb8503796b7d6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2017-08-20更新
|
577次组卷
|
7卷引用:2010-2011年江西省鄱阳县油墩街中学高二下学期期中考试理科数学
(已下线)2010-2011年江西省鄱阳县油墩街中学高二下学期期中考试理科数学(已下线)2011届广东省深圳高级中学高三上学期期中考试数学理卷(已下线)2013届云南玉溪一中高三上学期期中考试文科数学试卷江西省新余市2016-2017学年高二下学期期末质量检测数学(理)试题(已下线)2010-2011学年重庆市“名校联盟”高二第一次联考文科数学试卷(已下线)2012-2013学年山东省济宁市汶上一中高二12月质检理科数学试卷湖北省恩施州2019-2020学年高二上学期期末数学(理)试题
名校
解题方法
6 . 在平面直角坐标系xOy中,已知椭圆
:
的左,右焦点分别为
,
,点
是椭圆
在
轴上方的动点,且△
的周长为16.
(1)求椭圆
的方程;
(2)设点
到△
三边的距离均相等.
①当
时,求点
的坐标;
②求证:点
在定椭圆上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9740715ce186c32419647070c0716a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d0d2ff8333cdcb4d99d1e7e83698d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1414bd6928352a18c6d9d54f4e0f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5a8e1bc9748e5519dcd9981b7eb251.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5a8e1bc9748e5519dcd9981b7eb251.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fe6d8eb256935b3cd0ffab906778d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
②求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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名校
7 . 如图,两个椭圆的方程分别为
和
(
,
),从大椭圆两个顶点分别向小椭圆引切线
、
,若
、
的斜率之积恒为
,则椭圆的离心率为
![](https://img.xkw.com/dksih/QBM/2017/5/10/1683941226676224/1684004405100544/STEM/4aae2b13cb3a42769ccc1603be3af2d5.png?resizew=171)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9117cf794aed76e12165858898229b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634ed0b2e041e33ca4c86f05efc2a613.png)
![](https://img.xkw.com/dksih/QBM/2017/5/10/1683941226676224/1684004405100544/STEM/4aae2b13cb3a42769ccc1603be3af2d5.png?resizew=171)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2017-05-10更新
|
1247次组卷
|
2卷引用:江西省南昌市东湖区第十中学2019-2020学年高二上学期期中数学试题
名校
解题方法
8 . 已知椭圆
的中心在原点,焦点在
轴上,离心率为
,它的一个顶点恰好是抛物线
的焦点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/4/70b4b8f1-5298-4d59-97f6-3f2f556dec12.png?resizew=308)
(1)求椭圆
的方程;
(2)直线
与椭圆交于
两点,
点位于第一象限,
是椭圆上位于直线
两侧的动点.
①若直线
的斜率为
,求四边形
面积的最大值;
②当点
运动时,满足
,问直线
的斜率是否为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adbd62cb6779bc3b445dcbef97e3bf5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/4/70b4b8f1-5298-4d59-97f6-3f2f556dec12.png?resizew=308)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
②当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198c249705ffdee268cd836f382e3855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2016-12-03更新
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3卷引用:【全国百强校】江西省南昌市第二中学2018-2019学年高二上学期期中考试数学(文)试题
名校
9 . 已知椭圆
的两个焦点分别为
,以椭圆短轴为直径的圆经过点
.
(1)求椭圆
的方程;
(2)过点
的直线
与椭圆
相交于
两点,设点
,直线
的斜率分别为
,问
是否为定值?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae13b2a96f91ab64fb4948de2b0ae10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a724be4277e56ec8a770623aaa745e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fbad665fb13f72f65a071b9ea78318.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05526cb76b8ad1cd9ca14fb598e8c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0007b7a28aedee15e5f8388a15d1a7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe0ea445fc6b756b34b56a95e4d0381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5117784d5f7629ba7d20788328e6a1cd.png)
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2016-12-03更新
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1989次组卷
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18卷引用:江西省南昌市实验中学2017-2018学年高二上学期期中文科数学试题
江西省南昌市实验中学2017-2018学年高二上学期期中文科数学试题2015届四川省成都石室中学高三上期期中文科数学试卷【全国百强校】四川省成都市成都外国语学校2019届高三3月月考数学(理)试题2016届四川省成都市七中高三考试试卷2017届湖南长沙长郡中学高三入学考试数学(理)试卷河北省大名县第一中学2018届高三(实验班)上学期第一次月考数学(文)试题湖南省长沙市长郡中学2018届高三第四次月考数学(理)试题黑龙江省大庆实验中学2017-2018学年高二上学期期末考试数学(理)试题【全国百强校】四川省成都外国语学校2019届高三下学期3月月考试题 数学(文科)试题四川省成都外国语学校2019届高三下学期3月月考试题 数学(理)试题四川省成都市第七中学2019-2020学年高三上学期一诊模拟数学(文)试题四川省成都市第七中学2019-2020学年高三上学期一诊模拟数学(理)试题广东省深圳市红岭中学2020届高三上学期第二次统一考试数学(理)试题普通高等学校招生国统一考试2020-2021学年高三上学期 数学(文)考向卷(七)普通高等学校招生国统一考试 2020-2021学年高三上学期 数学(理)考向卷(七)(已下线)大题专练训练29:圆锥曲线(探索性问题1)-2021届高三数学二轮复习四川省内江市威远中学2020-2021学年高三1月月考数学(文)试题(已下线)专题16 圆锥曲线常考题型04——定值问题-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)
2010·广东汕头·一模
名校
10 . 已知抛物线、椭圆和双曲线都经过点
,它们在
轴上有共同焦点,椭圆和双曲线的对称轴是坐标轴,抛物线的顶点为坐标原点
![](https://img.xkw.com/dksih/QBM/2010/6/27/1569774870986752/1569774876368896/STEM/dc604be322e54c4f977a9f5c8f36b499.png?resizew=274)
(1)求这三条曲线的方程;
(2)已知动直线
过点
,交抛物线于
两点,是否存在垂直于
轴的直线
被以
为直径的圆截得的弦
长为定值?若存在,求出
的方程,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2595e01e8751886a27862cce04e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2010/6/27/1569774870986752/1569774876368896/STEM/dc604be322e54c4f977a9f5c8f36b499.png?resizew=274)
(1)求这三条曲线的方程;
(2)已知动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521d2cbdff8483ebba708857163ef1d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
长为定值?若存在,求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
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