名校
1 . 已知抛物线
的准线为
,点
在
上,且
到
的距离与
到原点
的距离相等.
(1)求
的方程;
(2)
是
上异于原点
的四个动点,且
,若
,垂足分别为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5718c4cf68779669eb41ff652b7e8a.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559fc5975418f34d3695f67b2ea45092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff8bb8c02ca9652683a42b48b5a8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
2022-03-31更新
|
1088次组卷
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4卷引用:山东省聊城市2022届高三一模数学试题
山东省聊城市2022届高三一模数学试题(已下线)专题二十四 抛物线(已下线)秘籍06 解析几何-备战2022年高考数学抢分秘籍(新高考专用)湖北省孝感市应城市第一高级中学2021-2022学年高三上学期8月热身考试数学试题
2 . 已知抛物线
,满足下列三个条件中的一个:①抛物线
上一动点
到焦点
的距离比到直线
的距离大1;②点
到焦点
与到准线
的距离之和等于7;③该抛物线
被直线
所截得弦长为16.请选择其中一个条件解答下列问题.
(1)求抛物线
的标准方程;
(2)
为坐标原点,直线
与抛物线
交于
,
两点,直线
的斜率为
,直线
的斜率为
,当
时,求
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f5c558d207fa59a2cab09c33399651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1e95fb519f59c46f40e4ab44660073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75f0d9463771a3aba1865a9d9d398aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cafe5616f3072141745891d3510f94c.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff189917311845175ee97c63e1bda32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
2021-05-09更新
|
777次组卷
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4卷引用:江苏省镇江市、湖北省华大新高考联盟2021届高三下学期模拟信息卷(一)数学试题
江苏省镇江市、湖北省华大新高考联盟2021届高三下学期模拟信息卷(一)数学试题(已下线)专题16 圆锥曲线中综合问题-2022年高考数学毕业班二轮热点题型归纳与变式演练(新高考专用)(已下线)热点12 圆锥曲线中综合问题-2022年高考数学【热点·重点·难点】专练(全国通用)陕西省渭南市韩城市2023-2024学年高二上学期期中数学试题
名校
解题方法
3 . 在平面直角坐标系中,
为坐标原点,抛物线
的焦点为
,抛物线
上不同两点
同时满足下列三个条件中的两个:①
;②
;③直线
的方程为
.
(1)请分析说明两点
满足的是哪两个条件?并求抛物线
的标准方程;
(2)若直线
与抛物线
相切于点
与椭圆
相交于
两点,
与直线
交于点
,以
为直径的圆与直线
交于
两点,求证:直线
经过线段
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083f25c5e40f66fd2686dbce367e382c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21946416f43b27fbe3bd23bc87d8b4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68831f427cd565ac3cc341024c9a422.png)
(1)请分析说明两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2533197f8ee31f7b77fb3db1929624ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d534c1b34556ff65910165035ea48d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1729d766f56cadd405bc12d57bcb1e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1729d766f56cadd405bc12d57bcb1e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b330da8d6528070cc1c4196c29c8569c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54d290009e138d1f0d4cb771cada9f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2021-05-27更新
|
574次组卷
|
3卷引用:山东省青岛市2021届高三三模数学试题
山东省青岛市2021届高三三模数学试题江苏省常州市前黄高级中学2021届高三下学期6月高考适应性考试(二)数学试题(已下线)考点64 章末检测九-备战2022年高考数学一轮复习考点帮(新高考地区专用)【学科网名师堂】
名校
解题方法
4 . 已知直线
与椭圆
交于
,
两点,且线段
的中点
恰好在抛物线
上.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712461595680768/2714493135052800/STEM/b43ba1b9-7707-47f9-bec2-33b38ee93e1b.png?resizew=294)
(1)若抛物线
的焦点坐标为
,求
的值;
(2)若过点
的直线
与抛物线
的另一交点为
,且
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18096b3646663bfc6e39ff38c3aff40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ab2192baa4c37dcf8d8e007b395f8c.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712461595680768/2714493135052800/STEM/b43ba1b9-7707-47f9-bec2-33b38ee93e1b.png?resizew=294)
(1)若抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f17aac6653dc966e7b76dd17fcc09d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bc10fb41577cd84641080ea2f23168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
您最近一年使用:0次
2021-05-05更新
|
513次组卷
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4卷引用:浙江省嘉兴市平湖市2021届高三下学期4月模拟测试数学试题
浙江省嘉兴市平湖市2021届高三下学期4月模拟测试数学试题湖南省衡阳市第八中学2021届高三下学期考前预测(三)数学试题全国Ⅱ卷决胜高考2021届高三数学(理)仿真卷试题(七)(已下线)专题11.平面解析几何(解答题)-《2022届复习必备-2021届浙江省高考冲刺数学试卷分项解析》