解题方法
1 . 已知椭圆C:
过点
,左右焦点为
,且椭圆C关于直线
对称的图形过坐标原点.
![](https://img.xkw.com/dksih/QBM/2017/3/13/1642757511905280/1648509036380160/STEM/1cf1f5d81c2f4cfd988d9789d23a8922.png?resizew=232)
(1)求椭圆C方程;
(2)圆D:
与椭圆C交于A,B两点,R为线段AB上任一点,直线F1R交椭圆C于P,Q两点,若AB为圆D的直径,且直线F1R的斜率大于1,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1721aa6b62fc4c68cb7161f2658117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f9772b3a117674e43222976a5dc816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a454588e9beb97c69a0332a7c5c796.png)
![](https://img.xkw.com/dksih/QBM/2017/3/13/1642757511905280/1648509036380160/STEM/1cf1f5d81c2f4cfd988d9789d23a8922.png?resizew=232)
(1)求椭圆C方程;
(2)圆D:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98b1a07df33a1fbbbec13b0187c9bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8634bf1cf55e8781167bc83d8a7288.png)
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2 . 设
(e为自然对数的底数),
.
(I)记
,讨论函数
单调性;
(II)令
,若函数G(x)有两个零点.
(i)求参数a的取值范围;
(ii)设
的两个零点,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47195ef7ff769c6e42c6cbc7c8f7076f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57f8297036689f06cf66bca379ad678.png)
(I)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37aa271a8c62d9ce6989f0f153c8716e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2316563595e29fd4279845ab8afc5ba2.png)
(II)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f4df397123ebc93c4cf732268c51bf.png)
(i)求参数a的取值范围;
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446fb08cd6399bd525f1aaf740b543c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b2c7b29e9cf77826549f38513ffc1e6.png)
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名校
解题方法
3 . 在平面直角坐标系
中,椭圆
:
的离心率是
,且直线
:
被椭圆
截得的弦长为
.
(Ⅰ)求椭圆
的标准方程;
(Ⅱ)若直线
与圆
:
相切:
(i)求圆
的标准方程;
(ii)若直线
过定点
,与椭圆
交于不同的两点
、
,与圆
交于不同的两点
、
,求
的取值范围.
![](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/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f6e613ffa032e7e893daa1970d3948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dcddf670657a860c55f0e17cd6c81a1.png)
(i)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(ii)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623afc24f2227004b0e1b3922dfb954b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/36ce018c92bc6bc8340f20ca7371d191.png)
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2017-03-13更新
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3185次组卷
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5卷引用:2017届山东省济宁市高三3月模拟考试数学文试卷
4 . 设
.
(1)令
,求
的单调区间;
(2)当
时,直线
与
的图像有两个交点
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11374e797c5e099a033c7863aa33d0f.png)
(1)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585de67a3fc494297d375d339af6d153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61f994d69c60e20f3cf7d9cfd6e66ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fbea4cd8b83daeb42afb389b0797b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475c9073257b3d0760e2c6051a82d592.png)
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5 . 已知椭圆
:
经过点
,离心率为
,点
为椭圆
的右顶点,直线
与椭圆相交于不同于点
的两个点
.
(Ⅰ)求椭圆
的标准方程;
(Ⅱ)当
时,求
面积的最大值;
(Ⅲ)若直线
的斜率为2,求证:
的外接圆恒过一个异于点
的定点.
![](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/6e684712aade8dcebb62716843791034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455bae796d928c3c4d9090e924259628.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5480fb837d606c40567242dad45b818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45b8b000c9c286bff8a480dbf03b513.png)
(Ⅲ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4bfa74832f9ad2afa8bad1135f67540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2017-03-10更新
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2卷引用:2017届山东省淄博市高三3月模拟考试数学理试卷
6 . 已知椭圆
,过点
作圆
的切线,切点分别为
.直线
恰好经过
的右顶点和上顶点.
(1)求椭圆
的方程;
(2)如图,过椭圆
的右焦点
作两条互相垂直的弦
,
.
①设
中点分别为
,证明:直线
必过定点,并求此定点坐标;
②若直线
,
的斜率均存在时,求由
四点构成的四边形面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51be38237df3982ee2615a2e20830e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502130506a08a4e04f179e69d3624367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7cc4adb3a12d91ecf32e47429c45af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcb20a6972108871adbf284f9e5006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(2)如图,过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28d2790a97390935125aa897417f970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999cb0e818df34be2c40f205ea6c6b7c.png)
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2017-02-08更新
|
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5卷引用:2017届山东枣庄市高三理上学期末期数学试卷
名校
7 . 已知函数
,曲线
在点
处的切线与直线
垂直(其中
为自然对数的底数).
(I)求
的解析式及单调递减区间;
(II)是否存在常数
,使得对于定义域内的任意
恒成立?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b248f2867ea97aaba545384f8535433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4769f7755429e5e1cfae9df9285e9317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f281814a940820e52ec332185871e22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(I)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(II)是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e48a6eea03d330733b2e327f02c6520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2016-12-04更新
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10卷引用:山东省日照第一中学2017届高三4月“圆梦之旅”(九)数学(文)试题
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2012·黑龙江·三模
8 . f(x)=lnx,g(x)=f(x)+f′(x).
(Ⅰ)求g(x)的单调区间和最小值;
(Ⅱ)讨论g(x)与
的大小关系;
(Ⅲ)求a的取值范围,使得g(a)﹣g(x)<
对任意x>0成立.
(Ⅰ)求g(x)的单调区间和最小值;
(Ⅱ)讨论g(x)与
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571758980046848/1571758985773056/STEM/08529206e94b4003bb50354b34197dae.png)
(Ⅲ)求a的取值范围,使得g(a)﹣g(x)<
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571758980046848/1571758985773056/STEM/9e59e1905c7647d194ec31b7792834a7.png)
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2016-12-03更新
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10卷引用:山东省烟台市2016-2017学年高二下学期期中学段考试数学(文)试题
山东省烟台市2016-2017学年高二下学期期中学段考试数学(文)试题2017届河南息县第一高级中学高三文上段测五数学试卷天津市耀华中学2018届高三上学期第一次月考数学(文)试题1【全国百强校】山东省济南第一中学2017-2018学年高二下学期期中考试数学(文)试题(已下线)2012届黑龙江省哈六中高三第三次模拟考试文科数学试卷(已下线)2011—2012学年江西省会昌中学高二下学期第二次月考文科数学试卷2011年普通高等学校招生全国统一考试文科数学(陕西卷)(已下线)2015届宁夏银川一中高三上学期第二次月考试卷文科数学试卷2019届黑龙江省哈尔滨市第六中学高三第四次模拟数学(文)试题海南热带海洋学院附属中学2021届高三11月第二次月考数学试题