名校
1 . 已知曲线
:
,抛物线
:
,
为曲线
上一动点,
为抛物线
上一动点,与两条曲线都相切的直线叫做这两条曲线的公切线,则以下说法正确的有___________
①直线l:
是曲线
和
的公切线:
②曲线
和
的公切线有且仅有一条;
③
最小值为
;
④当
轴时,
最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204a3630fd3f8c09f9d26e2857db37fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373a9b53140060a65450f09c1d1ac44c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
①直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
②曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35dff13f2d1a2e2631d3bb46892d17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34e01955f8c8fe2f0041b35d8d602a7.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d928238e1f1677f5f20ed62da87eb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88b7ab67adcb46f094b171881d98f26.png)
您最近一年使用:0次
2022-07-06更新
|
2281次组卷
|
8卷引用:北京市十一学校2021-2022学年高二下学期期末考试数学试题
北京市十一学校2021-2022学年高二下学期期末考试数学试题(已下线)专题19 圆锥曲线(讲义)-1北京市中国人民大学附属中学2023届高三上学期数学统练四试题四川绵阳市2022-2023学年高三二诊模拟考试(3)理科数学试题(已下线)期末考试押题卷01(考试范围:选择性必修第一册)-2022-2023学年高二数学新教材同步配套教学讲义(苏教版2019选择性必修第一册)(已下线)专题2 数形结合思想北京市第五十七中学2022-2023学年高二下学期3月月考数学试题(已下线)第13讲 抛物线(9大考点)(2)
2 . 平面直角坐标系中,过点
的圆
与直线
相切.圆心
的轨迹记为曲线
.
(1)求曲线
的方程;
(2)设
为曲线
上的两点,记
中点为
,过
作
的垂线交
轴于
.
①求
;
②当
时,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc13124d68e3eae80edb4a02da52d70b.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48867e261c61d24a0a1a4f7ff4627c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11417e967efe6ff509168e00eae6135a.png)
您最近一年使用:0次
3 . 已知抛物线
上的任意一点到
的距离比到x轴的距离大1.
(1)求抛物线的方程;
(2)若过点
的直线l与抛物线交于A,B两点,过A,B两点分别作抛物线的切线,两条切线交于点Q,求
重心G的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22840186db0afc0e2b2e8915ce79b998.png)
(1)求抛物线的方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
您最近一年使用:0次
解题方法
4 . 已知双曲线
的一条渐近线的方程为
,它的右顶点与抛物线
的焦点重合,经过点
且不垂直于
轴的直线与双曲线
交于
、
两点.
(1)求双曲线
的标准方程;
(2)若点
是线段
的中点,求点
的坐标;
(3)设
、
是直线
上关于
轴对称的两点,求证:直线
与
的交点必在直线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3302daceb2adfce2d7682a3557272922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5109d1f2e6464aeb82bda801de5b7034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0dfb7239aa52bb99a198b2d9bbf50e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(3)设
![](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/0fdc38632d93f9f67e377e36666baf79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ad96a0492c77ae833043352654a98b.png)
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5 . 在平面直角坐标系
中,已知点
到
的距离与到直线
的距离相等,记
的轨迹为
.
(1)求
的方程;
(2)
为坐标原点,轨迹
上两点
、
处的切线交于点
,
在直线
上,
、
分别交
轴于
、
两点,记
和
的面积分别为
和
.试探究:
是否为定值?若是定值,求出该定值;若不是定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2347bec7975dab2b8bce2fd19b1237d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](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/c5db41a1f31d6baee7c69990811edb9f.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd24f3c4bc9f9a75d4b28630bb630d2b.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/81dea63b8ce3e51adf66cf7b9982a248.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/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
6 . 如图,平面直角坐标系中,
,
,圆Q过坐标原点O且与圆L外切.若抛物线
与圆L,圆Q均恰有一个公共点,则p=______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c172d3811ba27a1e90a6c979b9ab79ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a1d8c54941b2a7d2ca0fe8f7cd7059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9de36529148d5e73cc4ff68b8f5e3fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/22/123ed3ad-30d6-4425-a125-5e68ef540c72.png?resizew=251)
您最近一年使用:0次
2022-06-20更新
|
1734次组卷
|
5卷引用:青海省2022届高三五月大联考理科数学试题
青海省2022届高三五月大联考理科数学试题(已下线)专题6 判断位置关系的运算(提升版)(已下线)专题14 圆锥曲线切线方程 微点3 圆锥曲线切线方程综合训练陕西省咸阳市永寿县中学2024届全国高考分科调研模拟测试数学(理)试题(二)(已下线)专题14 曲线与抛物线公切问题
解题方法
7 . 如图,已知F是抛物线
的焦点,过点F的直线与抛物线交于A,B两点,与圆O交于C,D两点(点A,C在第一象限),
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/18/ef9cd8b5-4daf-49c5-9d77-56fddafb07e7.png?resizew=248)
(1)求抛物线的方程;
(2)若
,求凹四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c9512a5409d8763e194e10953371a6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/18/ef9cd8b5-4daf-49c5-9d77-56fddafb07e7.png?resizew=248)
(1)求抛物线的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd82bf82c3254c27b00f65b9a697e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea96803d06a0d628e492b8d4edb2a02c.png)
您最近一年使用:0次
解题方法
8 . 已知抛物线
,其焦点为
,抛物线上有相异两点
,
.若
轴,则抛物线在
点处的切线经过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/0005c7ce-d5f8-4b50-a1a7-044c72a678b0.png?resizew=278)
(1)求抛物线的方程;
(2)若
,且线段
的中垂线交
轴于点
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfb2a536197b222df8b10a4c453f05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757e65bf99905cd6782c99392dc59024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef62e1ab66074b7967370421b3e34a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/0005c7ce-d5f8-4b50-a1a7-044c72a678b0.png?resizew=278)
(1)求抛物线的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1dc85723f64c4d545ccc4e4200fcab.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2022-06-14更新
|
320次组卷
|
2卷引用:2022年全国新高考II卷仿真模拟试卷(二)数学试题
解题方法
9 . 已知抛物线
上一点
(
)到焦点F的距离为5.
(1)求抛物线C的方程;
(2)过点F的直线l与抛物线C交于P,Q两点,直线OP,OQ与圆
的另一交点分别为M,N,O为坐标原点,求
与
面积之比的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d9c8906365dab3b6c65d845cc30075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
(1)求抛物线C的方程;
(2)过点F的直线l与抛物线C交于P,Q两点,直线OP,OQ与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd467734ec6674a00ae358e17cd4f77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
您最近一年使用:0次
解题方法
10 . 已知抛物线
的焦点为F,点
为抛物线上一点,抛物线C在点P处的切线与y轴相交于点Q,且
的面积为2.
(1)求抛物线的方程.
(2)若斜率不为0的直线l过焦点F,且交抛物线C于A,B两点,线段AB的中垂线与y轴交于点M,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d923eeca15176eed820f241a322eca3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a9bf6bda9363dbef5f6ff4bf6a5edf.png)
(1)求抛物线的方程.
(2)若斜率不为0的直线l过焦点F,且交抛物线C于A,B两点,线段AB的中垂线与y轴交于点M,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dfbfff309c30efa5e53710352fbc1f.png)
您最近一年使用:0次