名校
1 . 已知椭圆
的两个焦点坐标分别是
、
,并且经过点
.
(1)求椭圆
的方程;
(2)若直线
与圆
:
相切,并与椭圆
交于不同的两点
、
.当
,且满足
时,求
面积
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fbd80afc6c1f61eae4180d8786f250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02fa296072b97f77c00ca76fbf31f6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3051c32c6465c7ef45fbed78fe230339.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.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/69aa6a7790d21362f5f95a08aa5b0f63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75812683052e0f7499ac39a81bc918d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2981bf2261343f905ec1b5355a3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2017-02-08更新
|
2027次组卷
|
4卷引用:2016-2017学年湖南长郡中学高二上期中数学(理)试卷
名校
解题方法
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed762478d4c1460ea95a9dd9a201d1e.png)
(1)若
对任意的
恒成立,求实数
的取值范围;
(2)求证:对任意的
(
为自然对数的底数.
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed762478d4c1460ea95a9dd9a201d1e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求证:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f565470405badb641dc4058caf081aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e3ce576f0766f29349db973fc22eb8.png)
您最近一年使用:0次
2016-12-04更新
|
1056次组卷
|
2卷引用:湖南省长沙市雅礼中学2017-2018学年高二下学期期中数学(理)试题
3 . 已知等差数列
的前
项和为
,并且
,
,数列
满足:
,
,记数列
的前
项和为
.
(Ⅰ)求数列
的通项公式
及前
项和公式
;
(Ⅱ)求数列
的通项公式
及前
项和公式
;
(Ⅲ)记集合
,若
的子集个数为16,求实数
的取值范围.
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/cb6f27a9acdd470c81977e6564d40a6a.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/cc7db31974c342fd8d1738f5df8ae7f5.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/5e5bc0ea0785447898974fd2248f790f.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/090ea04fd5db41cdabc01f8420462278.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/2c69d055a89b4d0e963e351b31007872.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/a9570b0d47db4664b21bbfd4cefa749c.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/d80d0909ad3e41d79071c2f6e751461e.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/3f2bbded99984184bcf071ae06acfe3f.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/a9570b0d47db4664b21bbfd4cefa749c.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/cc7db31974c342fd8d1738f5df8ae7f5.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/b8fbb6598e9244279ea1b38a3db3d3b1.png)
(Ⅰ)求数列
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/cb6f27a9acdd470c81977e6564d40a6a.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/54612a515fbe40a5957b7d3cd9b6ecf6.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/cc7db31974c342fd8d1738f5df8ae7f5.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/5e5bc0ea0785447898974fd2248f790f.png)
(Ⅱ)求数列
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/a9570b0d47db4664b21bbfd4cefa749c.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/cbdd189ead16471eaa1512694e58f221.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/cc7db31974c342fd8d1738f5df8ae7f5.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/b8fbb6598e9244279ea1b38a3db3d3b1.png)
(Ⅲ)记集合
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/4058cf4f024241e39a64b745635cd468.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/48c32627a1b947dc81c49e977b97b71b.png)
![](https://img.xkw.com/dksih/QBM/2016/1/11/1572427887321088/1572427893555200/STEM/e70f3361a1fd404fa08bbca123a4adae.png)
您最近一年使用:0次
4 . 如图,
为椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
的左、右焦点,
是椭圆的两个顶点,椭圆的离心率
,
.若
在椭圆
上,则点
称为点
的一个“好点”.直线
与椭圆交于
两点,
两点的“好点”分别为
,已知以
为直径的圆经过坐标原点.
![](https://img.xkw.com/dksih/QBM/2016/1/5/1572416810254336/1572416815538176/STEM/20f864aa88c048c6bbf7bb0f2c125ede.png?resizew=203)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)△
的面积是否为定值?若为定值,试求出该定值;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b682c447054bc84b115a3ea80b928393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a8b4d8f329e5f702d3fee62737d047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2016/1/5/1572416810254336/1572416815538176/STEM/0de1862200424549a1b858257d5eed5e.png?resizew=8)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://img.xkw.com/dksih/QBM/2016/1/5/1572416810254336/1572416815538176/STEM/20f864aa88c048c6bbf7bb0f2c125ede.png?resizew=203)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
您最近一年使用:0次
名校
5 . 已知抛物线
:
(
)与椭圆
:
相交所得的弦长为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6ad069e39f9cbc01ede3772df24608.png)
(Ⅰ)求抛物线
的标准方程;
(Ⅱ)设
,
是
上异于原点
的两个不同点,直线
和
的倾斜角分别为
和
,当
,
变化且
为定值
(
)时,证明:直线
恒过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0aa23696b63c7d2d2950980a2c8cdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42713147196a377764d8c759c143208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d831e25098066aa3212d8695270de388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6ad069e39f9cbc01ede3772df24608.png)
(Ⅰ)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)设
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](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/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c62c14a017007a6bdfe25eada9c433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c62c14a017007a6bdfe25eada9c433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e197143a3210c70f87d5147128e80de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ab55147ca5c0f958af43b0637ee31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8db555926603fef963b1aa0e9111e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2016-10-28更新
|
1732次组卷
|
3卷引用:湖南省衡阳市第八中学2018-2019学年高二上学期期中数学(理)试题