在平面直角坐标系
中,已知椭圆
:
的离心率为
,短轴长为2.
![](https://img.xkw.com/dksih/QBM/2021/5/7/2716177558085632/2718689276895232/STEM/feed4877-2128-4149-993b-06cdf9cfebe4.png?resizew=293)
(1)求椭圆
的标准方程;
(2)设
为椭圆上顶点,点
是椭圆
上异于顶点的任意一点,直线
交
轴于点
,点
与点
关于
轴对称,直线
交
轴于点
.问:在
轴的正半轴上是否存在点
,使得
?若存在,求点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://img.xkw.com/dksih/QBM/2021/5/7/2716177558085632/2718689276895232/STEM/feed4877-2128-4149-993b-06cdf9cfebe4.png?resizew=293)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a12a125982972479eec216e903aad3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
2019高二下·浙江·学业考试 查看更多[4]
2019年浙江省普通高中学业水平名师预测卷(三)天津市耀华中学2021届高三下学期一模数学试题天津市第四十七中学2021-2022学年高三上学期第二次月考数学试题(已下线)考点巩固卷20 椭圆方程及其性质(十大考点)
更新时间:2021-05-11 12:10:24
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【推荐1】M是椭圆T:
1(a>b>0)上任意一点,F是椭圆T的右焦点,A为左顶点,B为上顶点,O为坐标原点,如下图所示,已知|MF|的最大值为3
,且△MAF面积最大值为3
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/bac97e15-3b20-4754-becc-747ef6407c92.png?resizew=199)
(1)求椭圆T的标准方程
(2)求△ABM的面积的最大值S0.若点N(x,y)满足x∈Z,y∈Z,称点N为格点.问椭圆T内部是否存在格点G,使得△ABG的面积S∈(6,S0)?若存在,求出G的坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22ecb9b0a87ab5098571bdf80441231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc34ae358bffe38f2a73ff3b3007b4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc34ae358bffe38f2a73ff3b3007b4ad.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/bac97e15-3b20-4754-becc-747ef6407c92.png?resizew=199)
(1)求椭圆T的标准方程
(2)求△ABM的面积的最大值S0.若点N(x,y)满足x∈Z,y∈Z,称点N为格点.问椭圆T内部是否存在格点G,使得△ABG的面积S∈(6,S0)?若存在,求出G的坐标,若不存在,请说明理由.
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【推荐2】椭圆E的方程为
,短轴长为2,若斜率为
的直线与椭圆E交于
两点,且线段
的中点为
.
(1)求椭圆E的方程;
(2)若直线l:
与圆
相切,且与椭圆E交于M,N两点,且
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3fda5d92d4f2a23a5c84f0855d0501.png)
(1)求椭圆E的方程;
(2)若直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d86a6026abea99737de584cd5edc55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3834dd00dbca1d1ec6729ddbd8647b.png)
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【推荐1】如图,椭圆
的一个焦点为
,且过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/23/9718925b-022f-4cad-a987-e258459c4670.png?resizew=172)
(1)求椭圆
的方程;
(2)若
为垂直于
轴的动弦,直线
与
轴交于点
,直线
与
交于点
.
(ⅰ)求证:点
恒在椭圆
上;
(ⅱ)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f363d815fde5c34c317df8c6a1d616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04147e15b00989da8277da4422f8b443.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/23/9718925b-022f-4cad-a987-e258459c4670.png?resizew=172)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(ⅰ)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
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【推荐2】已知椭圆
的左、右焦点分别为
、
,其离心率为
.椭圆
的左、右顶点分别为
,
,且
.
(1)求椭圆
的方程;
(2)过
的直线与椭圆相交于
,
(不与顶点重合),过右顶点
分别作直线
,
与直线
相交于
,
两点,以
为直径的圆是否恒过某定点?若是,求出该定点坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/57dfc9d1109fe41145cc892b5702d9fb.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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