名校
解题方法
1 . 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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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
2 . 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
|
1403次组卷
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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
3 . 已知椭圆![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/2ee635ed61f64f43a9163c377afd7ae3.png)
的左、右焦点分别为
,
,点
是椭圆的一个顶点,△
是等腰直角三角形.
(1)求椭圆
的方程;
(2)设点
是椭圆
上一动点,求线段
的中点
的轨迹方程;
(3)过点
分别作直线
,
交椭圆于
,
两点,设两直线的斜率分别为
,
,
且
,探究:直线
是否过定点,并说明理由.
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/2ee635ed61f64f43a9163c377afd7ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/5fb1220b9e6f4e29b7c0467fc223818c.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/47d098ea545d4db8937c28c2298c1de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb66dc6f2da7251ee614987a6066065e.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/af4be1f73e7946728115748313d2b9b3.png)
(1)求椭圆
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/c9065a20ab1449dab3f4b77055461278.png)
(2)设点
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/a5417e7e9af042e2b6abc79ddb7cfd8a.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/c9065a20ab1449dab3f4b77055461278.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/0bbfc554b7a14e08b5b2913eb9157593.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/2d972638b9e94bdb99a5fac9a2a3ba0e.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/6f61a6d5165e465fb47848d6b6a0ad7c.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/7326663c7b4c447a9537cd3505244366.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/01e9fd37d7af450e81849417368affc8.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/43c9b5d2943744eba1aded20523edcca.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/2226e793d21847f7bc0c1ce6a3732508.png)
![](https://img.xkw.com/dksih/QBM/2015/12/30/1572409109168128/1572409114886144/STEM/8164938206024862811895c783d19922.png)
且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b1bd378406bcd8156a56469f9300f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2016-12-03更新
|
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|
2卷引用:2016上海复旦大学附中届高三上期中文科数学试卷
名校
解题方法
4 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88c051b4ce8554351dccf68d681b4a.png)
(
)的离心率为
,右焦点到直线
的距离为
.
(1)求椭圆
的方程;
(2)已知点
,斜率为
的直线
交椭圆
于两个不同点
.
,设直线
与
的斜率分别为
,
,①若直线
过椭圆
的左顶点,求此时
,
的值;②试猜测
,
的关系,并给出你的证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88c051b4ce8554351dccf68d681b4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db093fbae76df48260f2dac6d743558.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e456c4c036ed08176d0cbbdad36cfb87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db093fbae76df48260f2dac6d743558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f7333f8270f43dbe6c250184edc36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7a2e98986f82571b0408d9b451a345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5836228c25fc38e22ce246fae56186a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a48b4f2605970638a8f4909de2cba7c.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db093fbae76df48260f2dac6d743558.png)
![](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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
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2016-12-03更新
|
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|
2卷引用:2015届山东省烟台市高三下学期一模文科数学试卷
2013·江西新余·模拟预测
5 . 已知中心在原点,焦点在坐标轴上的椭圆
的方程为
它的离心率为
,一个焦点是(-1,0),过直线
上一点引椭圆
的两条切线,切点分别是A、B.
(1)求椭圆
的方程;
(2)若在椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b256f697ce288c5c33e24806ca540cc.png)
上的点
处的切线方程是
.求证:直线AB恒过定点C,并求出定点C的坐标;
(3)是否存在实数
,使得求证:
(点C为直线AB恒过的定点).若存在
,请求出,若不存在请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b256f697ce288c5c33e24806ca540cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6c03da0d896079b97c4a208d714be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b256f697ce288c5c33e24806ca540cc.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b256f697ce288c5c33e24806ca540cc.png)
(2)若在椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b256f697ce288c5c33e24806ca540cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ec56b59d6f2654570c2b5c4fd13a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6a4781b020b879519321e05c299f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9656735f55e5de465e5667ba578d4e.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fffd330dd6b9241659d790bd2a7fb2.png)
![](https://img.xkw.com/dksih/QBM/2013/4/10/1571181206159360/1571181211959296/STEM/9dcb5183efd4433a94c5c3a0b4cd461d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fffd330dd6b9241659d790bd2a7fb2.png)
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2016-12-03更新
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