1 . 已知斜率为1的直线
过椭圆
的右焦点,交椭圆于
两点,则弦
的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-10-25更新
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1074次组卷
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6卷引用:专题3.5 直线与椭圆的位置关系-重难点题型精讲-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)
(已下线)专题3.5 直线与椭圆的位置关系-重难点题型精讲-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)江西省贵溪市实验中学2022届高三上学期第二次月考(三校生)数学试题甘肃省张掖市民乐县第一中学2021-2022学年高二上学期期中数学理科试题(已下线)第63讲 直线与圆锥曲线河南省驻马店市新蔡县第一高级中学2021-2022学年高二上学期12月月考数学(理科)试题(已下线)第五节 椭圆 第二课时 直线与椭圆的位置关系 A素养养成卷
2 . 在平面直角坐标系
中,
,
,C是满足
的一个动点.
(1)求
垂心H的轨迹方程;
(2)记
垂心H的轨迹为
,若直线l:
(
)与
交于D,E两点,与椭圆T:
交于P,Q两点,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca22d434c8671cf39eba5fa03b31ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2d7ff2b15c4e93fe6b92baca3c76d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2a8d0c77c54fdf9aa97978f8e5dc0b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f6978eb6a3f71949b240260be84351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad847293e9c58676607222f35b0395ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b43cb8c0f6c3d7be3ad775acfc3117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0101f71b8868072edef8f80040fc76.png)
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2021-09-06更新
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4卷引用:广东省2022届高三上学期调研仿真数学试题
广东省2022届高三上学期调研仿真数学试题(已下线)专题40 轨迹方程求解方法-学会解题之高三数学万能解题模板【2022版】(已下线)热点10 直线与圆-2022年高考数学【热点·重点·难点】专练(全国通用)全国新高考2021届高三数学方向卷试题(A)
名校
解题方法
3 . 为了监测某海域的船舶航行情况,海事部门在该海域,设立了如图所示东西走向,相距
海里的
,
两个观测站,观测范围是到
,
两观测站距离之和不超过
海里的区域.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/c2a373ba-06d1-4e31-81b6-d10c53ad7ee3.png?resizew=164)
(1)以
所在直线为
轴,线段
的垂直平分线为
轴建立平面直角坐标系,求观测区域边界曲线的方程;
(2)某日上午7时,观测站B发现在其正东10海里的C处,有一艘轮船正以每小时8海里的速度向北偏西45°方向航行,问该轮船大约在什么时间离开观测区域?(精确到1小时).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b72ac611ae66b86761e080761d9aabc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/c2a373ba-06d1-4e31-81b6-d10c53ad7ee3.png?resizew=164)
(1)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)某日上午7时,观测站B发现在其正东10海里的C处,有一艘轮船正以每小时8海里的速度向北偏西45°方向航行,问该轮船大约在什么时间离开观测区域?(精确到1小时).
您最近一年使用:0次
2021-08-16更新
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342次组卷
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2卷引用:浙江省北斗星盟2022-2023学年高二上学期12月阶段性联考数学试题
4 . 已知点
,
,
的周长等于
,点
满足
.
(1)求点
的轨迹
的方程;
(2)是否存在过原点的直线
与曲线
交于
,
两点,与圆
交于
,
两点(其中点
在线段
上),且
,若存在,求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c77a42750684cb6157c2c7fb9422a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a56e5ddc6dc057aa4076130cc6ce19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388590e0f8d9dfeaf2b65f80648257d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2176a2e99464c2ea5aa74112fc3c8d83.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)是否存在过原点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e422684db249ade9cce0bf7a627f7ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4bff6dcb78b9cfad8aeb2907b8292e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2021-08-14更新
|
865次组卷
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5卷引用:专题20 椭圆、抛物线(解答题)-备战2022年高考数学(理)母题题源解密(全国甲卷)
(已下线)专题20 椭圆、抛物线(解答题)-备战2022年高考数学(理)母题题源解密(全国甲卷)(已下线)专题21 椭圆、抛物线(解答题)-备战2022年高考数学(文)母题题源解密(全国甲卷)江西省南昌市2022届高三下学期核心模拟卷(中)数学(文)试题云南省曲靖市2021届高三二模数学(文)试题江苏省南京市金陵中学2021-2022学年高三上学期学情检测考前热身数学试题
21-22高二上·浙江·期末
名校
解题方法
5 . 如图,已知抛物线
,椭圆
:中心在原点,焦点在y轴上,且离心率为
.直线
交
于A、B两点,交
于M、N两点.
是
上的点,且始终位于直线l的右上方.连接
、
,
的平分线交y轴于H,交
的左侧部分于T.
![](https://img.xkw.com/dksih/QBM/2021/4/29/2710480269828096/2710520303804416/STEM/18ff74aa68284d80b779362a4c1110a8.png?resizew=231)
(1)求证:
轴;
(2)若M是
的中点,
是否存在最大值?若存在,求出使
取得最大值时m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cf08f835978859030ed7aceabafc27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b631f0160d1e977e798bac3440d2d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a75680a9e16ed607cdea14b4b367fd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/2021/4/29/2710480269828096/2710520303804416/STEM/18ff74aa68284d80b779362a4c1110a8.png?resizew=231)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5a06e64be51ec0ea71356b000a9b.png)
(2)若M是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4638ad26fd816ec06abd5eb1c455e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4638ad26fd816ec06abd5eb1c455e6.png)
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