名校
解题方法
1 . 如图,已知椭圆
经过点
,离心率
.
的标准方程;
(2)椭圆
上任意点
轴上一点
,若
的最小值为
,求实数
的取值范围;
(3)设
是经过右焦点
的任一弦(不经过点
),直线
与直线
相交于点
,记
的斜率分别为
,求证:
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04147e15b00989da8277da4422f8b443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81828dcd00a71cf376e8003488886bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f959ea4e8be882517c570b7bd7ad0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce0dbfbaede9bcbc415a105e36688e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c58b986bea8854118adc80af4437ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166a8e1bcb93423697696e2ba0409fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf3a71536f4f45cd75732e8b48592eb.png)
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2024-03-29更新
|
474次组卷
|
4卷引用:上海市松江二中2023-2024学年高二下学期期中数学试卷
上海市松江二中2023-2024学年高二下学期期中数学试卷上海市向明中学2023-2024学年高二下学期3月月考数学试题(已下线)专题02圆锥曲线全章复习攻略--高二期末考点大串讲(沪教版2020选修一)湖北省武汉市第二中学2023-2024学年高三下学期模拟考试(最后一卷)数学试卷
名校
解题方法
2 . 太曲线
由曲线
和曲线
组成,其中点
、
为曲线
所在圆锥曲线的焦点,点
、
为曲线
所在圆锥曲线的焦点.
,
,求曲线的方程;
(2)作曲线
第一象限中渐近线的平行线
,若与曲线
有两个公共点
、
,求证:弦
的中点
必在曲线
的另一条渐近线上;
(3)设
,
,若直线
过点
交曲线
于点
,求
的面积
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68294f6f91613d44dbd4b22c24a76220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abeacbd3604d4e926b8d2ffe370f5322.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1282962a17a48a18edf733204054d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13683e2ecf2164a0adbfdb9923d210a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43fc57c70b00a6f9906bf9369ef7c28.png)
(2)作曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fcc480016747ca3595a20507ff3c2c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3320a13248a3a1208ff6ee85c9d26f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdbb45d7359537458736c9ea5bf9e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2024-03-12更新
|
246次组卷
|
3卷引用:上海市第二中学2023-2024学年高二下学期期中数学试题
上海市第二中学2023-2024学年高二下学期期中数学试题上海交通大学附属中学2023-2024学年高二下学期摸底数学试卷(已下线)专题02圆锥曲线全章复习攻略--高二期末考点大串讲(沪教版2020选修一)
名校
3 . 方程
表示焦点在
轴上的椭圆,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353ba94a6e980c4667b647644fbb7703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-02-23更新
|
561次组卷
|
5卷引用:上海市华东师范大学第三附属中学2023-2024学年高二下学期期中考试数学试题
上海市华东师范大学第三附属中学2023-2024学年高二下学期期中考试数学试题上海市华东师范大学第二附属中学2023-2024学年高二上学期期末考试数学试卷上海市嘉定区第二中学2023-2024学年高二下学期3月月考数学试题上海市扬子中学2023-2024学年高一下学期期中考试数学试题(已下线)专题04 圆锥曲线(六大题型+优选提升题)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)
4 . 已知椭圆C:
的离心率为
,左、右顶点分别为A、B,过点
的直线与椭圆相交于不同的两点P、Q(异于A、B),且
.
(1)求椭圆C的方程;
(2)若直线AP、QB的斜率分别为
、
,且
,求
的值;
(3)设
和
的面积分别为
、
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d195911a91d12edd5685f6cd963fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dddd06a88839dc33edcea74128743ae.png)
(1)求椭圆C的方程;
(2)若直线AP、QB的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bc0ee0a95fab04edf648026f14b9ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a551505ae42b49904bab59b17012d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9c5ae63072e1684cf1c242c8133d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59c4295f918205f5598ecc9a96d8867.png)
您最近一年使用:0次
2024-01-19更新
|
397次组卷
|
4卷引用:上海市华东师范大学第三附属中学2023-2024学年高二下学期期中考试数学试题
名校
5 . 已知
,
,则方程
表示焦点在x轴上的椭圆的概率是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae32d7b43e253673053bad4a69197ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1542c48f287494f0c5f70a5c9eb6bfd.png)
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名校
解题方法
6 . 已知椭圆
的左,右焦点分别为
,下顶点为A,点M在直线
上.
(1)若
,线段AM 的中点在x轴上,求M 的坐标;
(2)若直线l与y轴交于B,直线AM 经过右焦点
,在
中有一个内角的余弦值为
,求b的值;
(3)若
,直线 l与椭圆Γ没有公共点,在椭圆Γ上存在一点
,
,点P到l的距离为d,且
,当a变化时,求d的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e31f17d3eae2f76500ee2e8f955865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f49644cd9fa4688cc3a74a234952530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a029686de8da4b04df32af401089a9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa5584ebddd742ffcf0e58a4c3b108c.png)
(2)若直线l与y轴交于B,直线AM 经过右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc97864dd9abe8013867fdd6b9562c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386ddd7cba3dc92cb43743f663ae63d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0ca9a39621967d7ba5629ea9b12d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c318dc642320a42ad8f7c565246858b5.png)
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7 . 已知动圆
经过定点
,且与圆
:
内切.
(1)求动圆圆心
的轨迹
的方程;
(2)设轨迹
与
轴从左到右的交点为
,
,点
为轨迹
上异于
,
的动点,设
交直线
于点
,连接
交轨迹
于点
,直线
,
的斜率分别为
,
.
①求证:
为定值;
②证明:直线
经过
轴上的定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866502435d9ea08c6d3a5e304a8986c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8387b687579c4d5152175c9d19e24232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9811dd726ed27d28ad5a8e83fbb20ed6.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设轨迹
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef79861421b414b455a090a3ef04fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b51a4949896526cfc3c076ea8dec8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128147bd4834566a78b4e9d2a3b2139c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4a51e6728d354cc1c3d32e2d4368d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729d727db2181aca4e8a6455d10cfe28.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6b1769274eee3ce2896cb3513d50f8.png)
②证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2024-01-11更新
|
630次组卷
|
11卷引用:上海奉贤区致远高级中学2022-2023学年高二下学期期中数学试题
8 . 对于曲线C:
,给出下列命题:(1)曲线关于原点中心对称;(2)
,
;(3)曲线C恒在直线
的上方;(4)对于曲线上任意两点
,
,都有
;(5)直线
与曲线C最多有两个不同的公共点.则其中真命题的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/474b5ec72ba456745109c1a76749af74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cefa22307df0766668749b924a82597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cd2a180ae300bbf2388a709e4c28e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56720e2f2b0ddd72156da495923698da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2852ae85cfcc804b3192ea8543c88938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48418567df7e02c8b85d5460a5a31c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e19b6ec791d3f5e638815551c326775.png)
A.0个 | B.1个 | C.2个 | D.3个 |
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名校
9 . 试讨论方程
所表示的曲线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09e849ec3ca357657fd12187b8fb461.png)
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解题方法
10 . 已知椭圆的对称轴为坐标轴,一个焦点坐标为
,且椭圆的两个焦点和短轴的一个端点构成一个等腰直角三角形,则此椭圆的标准方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
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