1 . 已知点
在抛物线
的准线上,过点
作直线
与抛物线
交于
两点,斜率为2的直线与抛物线交于
两点.
(1)求抛物线
的标准方程;
(2)① 求证:直线
过定点
;
② 若
的面积为
,且满足
,求直线
斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc2de9df8bce6139613bb86322db0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e478787ebfeb68a5a7594dbd9eecd4.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)① 求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
② 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c8bef41fa6778e5eb57e2f19ea48f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-01-27更新
|
259次组卷
|
3卷引用:江苏省徐州市沛县第二中学2024届高三下学期期初测试数学试题
江苏省徐州市沛县第二中学2024届高三下学期期初测试数学试题湖北省武汉外国语学校2023-2024学年高二上学期期末考试数学试题(已下线)2.4.2 抛物线的性质(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
名校
解题方法
2 . 设抛物线
的焦点为
,过点
的直线与抛物线交于
两点.
(1)若
,求线段
中点
的轨迹方程;
(2)若直线
的方向向量
,当焦点为
时,求
的面积;
(3)若
是抛物线
准线上的点,直线
,
,
的斜率分别为
,
,
,求证:
为
的等差中项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e677a11b56f7912f9bd0fadcf2a272b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a950eeebd15f01acf65ea8ebdca944a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7b76d897de678faaf8221bafe217d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.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/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
您最近一年使用:0次
3 . 已知抛物线
为抛物线外一点,过点
作抛物线的两条切线,切点分别为
(
在
轴两侧),
与
分别交
轴于
.
(1)若点
在直线
上,证明直线
过定点,并求出该定点;
(2)若点
在曲线
上,求四边形
的面积的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0a6c9f4ef3b0036a1df6e81df813ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d0aa9412dd7caf42cc71520e282328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08946c671242c2e88e89fd542704bb3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa76cfd79a2ff6b28f370e54f4eb51d.png)
您最近一年使用:0次
2023-12-02更新
|
2768次组卷
|
7卷引用:山东省临沂市费县2024届高三下学期开学考试数学试题
山东省临沂市费县2024届高三下学期开学考试数学试题湖南省长沙市周南中学2023-2024学年高二下学期入学考试数学试题2024届湖南省高三九校联盟第一次联考数学试卷(已下线)模块六 全真模拟篇 拔高2 期末终极研习室(2023-2024学年第一学期)高三河南省南阳市第一中学校2024届高三上学期第六次月考数学试题2024年1月“九省联考”仿真卷数学试题(已下线)专题18 圆锥曲线高频压轴解答题(16大核心考点)(讲义)-1
4 . 设抛物线
:
的焦点为
,经过
轴正半轴上点
的直线
交
于不同的两点
和
.
![](https://img.xkw.com/dksih/QBM/2023/9/16/3325927705313280/3326673693712384/STEM/1223ed506a3e4f039801215c1fc65a90.png?resizew=164)
(1)若
,求
点的坐标;
(2)若
,求证:原点
总在以线段
为直径的圆的内部;
(3)若
,且直线
,
与
有且只有一个公共点
,问:
的面积是否存在最小值?若存在,求出最小值,并求出
点的坐标;若不存在,请说明理由.(三角形面积公式:在
中,设
,
,则
的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62769b7177ef4bc952dc1dd51d6b510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2023/9/16/3325927705313280/3326673693712384/STEM/1223ed506a3e4f039801215c1fc65a90.png?resizew=164)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48276435f2fa9c0e510be76df906b96e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1683899c08a58eeb25a917dfab3e7b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88c9366bb209931c6b28353dbab9a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49830e1af740638d68a1c06379e4ae04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bac07538f25bb48ed4853686c3a8a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58ad468fd2b5c4523ec51c27e9c1452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945d04f80a276efbfadf0d1f23512075.png)
您最近一年使用:0次
5 . 已知抛物线
的焦点为
,过
的直线
交
于
两点,过
与
垂直的直线交
于
两点,其中
在
轴上方,
分别为
的中点.
(1)证明:直线
过定点;
(2)设
为直线
与直线
的交点,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764c199d659322854377a92fee97642d.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102716b8d55b91adb37dfe019cc7231b.png)
您最近一年使用:0次
2024-01-19更新
|
6982次组卷
|
8卷引用:福建省厦门双十中学2023-2024学年高二下学期开学考试数学试题
福建省厦门双十中学2023-2024学年高二下学期开学考试数学试题2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19广东省惠州市第一中学2024届高三上学期第三次阶段测试数学试题2024年九省联考试卷分析及真题鉴赏(已下线)专题18 圆锥曲线高频压轴解答题(16大题型)(练习)(已下线)专题07 双曲线与抛物线(分层练)(五大题型+12道精选真题)(已下线)专题08 圆锥曲线 第二讲 圆锥曲线中的定点、定直线与定值问题(解密讲义)
6 . 已知抛物线
的焦点为F,
,点
是在第一象限内
上的一个动点,当DP与
轴垂直时,
,过点
作与
相切的直线
交
轴于点
,过点
作直线
的垂线交抛物线
于A,B两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/3/c6277961-e5d6-4df3-9800-7b451fa56dfb.png?resizew=150)
(1)求C的方程;
(2)如图,连接PD并延长,交抛物线C于点Q.
①设直线AB,OQ(其中O为坐标原点)的斜率分别为
,
,证明:
为定值;
②求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ee8669bc280bff4b20644cb82faf23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46906f6684fdac35dc6f3ffebd495ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/3/c6277961-e5d6-4df3-9800-7b451fa56dfb.png?resizew=150)
(1)求C的方程;
(2)如图,连接PD并延长,交抛物线C于点Q.
①设直线AB,OQ(其中O为坐标原点)的斜率分别为
![](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/67351fe10fcfc3f9072eec4c60bfaaa5.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2159546c9b881101210737a2b0ff4a.png)
您最近一年使用:0次
2023-05-02更新
|
1058次组卷
|
3卷引用:四川省宜宾市第四中学校2023-2024学年高三上学期开学考试理科数学试题
21-22高二·全国·课后作业
7 . 如图,过抛物线x2=y上任意一点P(不是顶点)作切线l,l交y轴于点Q.
![](https://img.xkw.com/dksih/QBM/2022/1/5/2887837457678336/2953219552477184/STEM/15dfd8ef-1338-4fbb-bdc4-9f6b6c151084.png?resizew=216)
(1)求证:线段PQ的中垂线过定点;
(2)过直线y
x﹣1上任意一点R作抛物线x2=y的两条切线,切点分别为S、T,M为抛物线上S、T之间到直线ST的距离最大的点,求△MST面积的最小值.
![](https://img.xkw.com/dksih/QBM/2022/1/5/2887837457678336/2953219552477184/STEM/15dfd8ef-1338-4fbb-bdc4-9f6b6c151084.png?resizew=216)
(1)求证:线段PQ的中垂线过定点;
(2)过直线y
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c70c0c5a061195b9941796b6a9acc4.png)
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2022-04-07更新
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3卷引用:四川省成都市蓉城名校联盟2021-2022学年高三上学期入学联考理科数学试题
四川省成都市蓉城名校联盟2021-2022学年高三上学期入学联考理科数学试题四川省成都市蓉城名校联盟2021-2022学年高三上学期入学联考数学(文)试题(已下线)专题3.14 直线与抛物线的位置关系-重难点题型检测-2021-2022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)
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解题方法
8 . 如图,直线
与抛物线
相交于不同的两点
、
,且
(
为定值),线段
的中点为
,与直线
平行的抛物线
的切线的切点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/617162a9-7660-483c-a305-ce709a94c513.png?resizew=223)
(1)用
、
表示出点
、点
的坐标,并证明
垂直于
轴;,
(2)求
的面积(只与
有关,与
、
无关);
(3)小张所在的兴趣小组完成上面两个小题后,小张连
、
,再作与
、
平行的切线,切点分别为
、
,小张马上写出了
、
的面积,由此小张求出了直线
与抛物线围成的面积,你认为小张能做到吗?请你说出理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24e616b5a35ff372c78c1472f156ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6bd75ceb16bfdd32914cb58b9dceca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/617162a9-7660-483c-a305-ce709a94c513.png?resizew=223)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)小张所在的兴趣小组完成上面两个小题后,小张连
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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9 . 已知抛物线
的焦点为F,以F和准线上的两点为顶点的三角形是边长为
的等边三角形,过
的直线交抛物线E于A,B两点.
(1)求抛物线E的方程;
(2)是否存在常数
,使得
,如果存在,求
的值,如果不存在,请说明理由;
(3)证明:
内切圆的面积小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c42d88e496a17562d25195301e0ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f83dbfddc6f98548699ed581e8c8608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ab82c33e6c1f8b73628fa78e6868b4.png)
(1)求抛物线E的方程;
(2)是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33104cb3b15fa0e01842e78f9ed59701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
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2022-02-13更新
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3卷引用:浙江省温州市瑞安市第六中学2021-2022学年高二下学期入学检测数学试题 .
10 . 在平面直角坐标系
中,抛物线
,点
,
,
为
上的两点,
在第一象限,满足
.
(1)求证:直线
过定点,并求定点坐标;
(2)设
为
上的动点,求
的取值范围;
(3)记△
的面积为
,△
的面积为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1354240a807d0da2b51a19e055140165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37df9dad3961893b22d6639c4311e267.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/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46cd485957ac7c628785ca04a60e1aaf.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e368d77f94bb058d2480f122f44ea366.png)
(3)记△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa3a310c1f8a5af35dc3328d874e18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c21cbb1c2bcbcb8391ac5a879f2ae0.png)
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