解题方法
1 . 如图,已知椭圆
:
(
),且离心率为
,抛物线
:
(
).点
是椭圆
与抛物线
的交点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/02fbb7fc-cae7-40a9-9cbc-1f0b158deedc.png?resizew=172)
(1)求曲线
和曲线
的方程;
(2)过点P作斜率为k(
)的直线
交椭圆
于点A,交抛物线
于点B(A,B异于点P).
①若
,求直线
的方程;
②过点P作与直线
的倾斜角互补的直线
,且直线
交抛物线
于点C,交椭圆
于点D(C,D异于点P).记
的面积为
,
的面积为
.若
,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/02fbb7fc-cae7-40a9-9cbc-1f0b158deedc.png?resizew=172)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)过点P作斜率为k(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4eaa80b44625890339d6a0065c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb3837ed99dbdc05cc7b718a600c969d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
②过点P作与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62b61e5137a0e15d878b502ba957117.png)
您最近一年使用:0次
2 . 已知椭圆C:
(
)经过
,
两点.O为坐标原点,且
的面积为
.过点
且斜率为k(
)的直线l与椭圆C有两个不同的交点M,N,且直线
,
分别与y轴交于点S,T.
(Ⅰ)求椭圆C的方程;
(Ⅱ)求直线l的斜率k的取值范围;
(Ⅲ)设
,
,求
的取值范围.
![](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/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c09615735d331befd07664aa47cb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
(Ⅰ)求椭圆C的方程;
(Ⅱ)求直线l的斜率k的取值范围;
(Ⅲ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cfc9b28711b4e9c4b554202fe46fe6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bd0693e932eb65b222f3453e04280b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
2020-06-23更新
|
1315次组卷
|
8卷引用:江苏省苏州市常熟中学2019-2020学年高一(15.16班)下学期六月质量检测数学试题
名校
解题方法
3 . 如图,定义:以椭圆中心为圆心,长轴为直径的圆叫做椭圆的“辅圆”.过椭圆第一象限内一点P作x轴的垂线交其“辅圆”于点Q,当点Q在点P的上方时,称点Q为点P的“上辅点”.已知椭圆
上的点
的上辅点为
.
![](https://img.xkw.com/dksih/QBM/2020/3/7/2414498881355776/2416112467918848/STEM/0bc76bd9659847feb12e379fac458f85.png?resizew=262)
(1)求椭圆E的方程;
(2)若
的面积等于
,求上辅点Q的坐标;
(3)过上辅点Q作辅圆的切线与x轴交于点T,判断直线PT与椭圆E的位置关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedad6bb70631b944c69f8f0b02b35d6.png)
![](https://img.xkw.com/dksih/QBM/2020/3/7/2414498881355776/2416112467918848/STEM/0bc76bd9659847feb12e379fac458f85.png?resizew=262)
(1)求椭圆E的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45b8b000c9c286bff8a480dbf03b513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(3)过上辅点Q作辅圆的切线与x轴交于点T,判断直线PT与椭圆E的位置关系,并证明你的结论.
您最近一年使用:0次
2020-03-10更新
|
348次组卷
|
2卷引用:2020届江苏省苏州市高三上学期期末数学试题
名校
4 . 设中心在原点O,焦点在x轴上的椭圆C过点
,F为C的右焦点,⊙F的方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c568fff654042da15d5653c932df3d.png)
(1)求C的方程;
(2)若直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840c25e241ff99bf4bf940ddeb7ade39.png)
与⊙O相切,与⊙F交于M、N两点,与C交于P、Q两点,其中M、P在第一象限,记⊙O的面积为
,求
取最大值时,直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b87b151f60a54dc8156a69b145bb866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c568fff654042da15d5653c932df3d.png)
(1)求C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840c25e241ff99bf4bf940ddeb7ade39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b377f632949bff36083a5464113387fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3465f50ce6b7704c17846758413f00d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45456df9db47262a717951fb28556d3.png)
您最近一年使用:0次
2020-02-01更新
|
467次组卷
|
6卷引用:2020届山东省枣庄、滕州市高三上学期期末考试数学试题
2020届山东省枣庄、滕州市高三上学期期末考试数学试题江苏省南通市2020-2021学年高三上学期12月月考模拟测试数学试题江苏省苏州大学附属中学2020-2021学年高二下学期3月月考数学试题(已下线)黄金卷08 【赢在高考·黄金20卷】备战2021年高考数学全真模拟卷(广东专用)江苏省扬州大学附属中学2020-2021学年高三上学期1月阶段检测数学试题山东省枣庄市第三中学2022-2023学年高三上学期期中考试数学试题
解题方法
5 . 平面直角坐标系
中,已知椭圆
过点
,离心率为
.
(1)求椭圆
的方程;
(2)设直线
与椭圆
交于
,
两点.
①若直线
过椭圆
的右焦点,记
三条边所在直线的斜率的乘积为
,求
的最大值;
②若直线
的斜率为
,试探究
是否为定值,若是定值,则求出此定值;若不是定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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)
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c325b9535c92eb2ece4650df93197d.png)
您最近一年使用:0次