名校
解题方法
1 . 已知点
, 在抛物线
上任取一点
,作
轴,垂足为
,
的最小值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885e3f2fb6994977ae6d9d8425613da8.png)
(1)求
;
(2)已知圆
,设
(
且
)为圆
外一点,过点
作圆
的两条切线
和
,
交
于两个不同的点
,
,
交抛物线
于两个不同的点
,
,且
,求点
的轨迹方程,并求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37bbde2076bfa6dd859f7787e155ab8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6dbffaf5a3fc708f23bf6e44cbc25a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb509a172e9821b63370f178d06dc2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885e3f2fb6994977ae6d9d8425613da8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948811debe828137d751f874107b6cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/379be5b2433ea5a4ff2f32537459948c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe8dc8e5def7d46b88535453ae1fd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d14d14310aaf4630c169e8d7b2a9cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34494f6910d4e081d89d1136c8cdff4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce425bceb12b035f4ea44ebcd5f4519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d341082cc54b1cb7a790af9ec4a365d.png)
您最近一年使用:0次
解题方法
2 . 已知曲线
由抛物线
及抛物线
组成,若
是曲线
上关于
轴对称的两点,
四点不共线,其中点
在第一象限.
(1)写出抛物线
的焦点坐标和准线方程;
(2)求四边形
周长的最小值;
(3)若点
横坐标小于4,求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafae84e7fe39dc5b694c39405201d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b8c4f0b6727072be4e51cf419a4d8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c99123b111d541e6246db52514bd384.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/0f63a76a5f78eb64e64b5a2c9f1553cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)写出抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafae84e7fe39dc5b694c39405201d32.png)
(2)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
3 . 已知,点
分别是抛物线
的焦点与曲线上一动点,点
在抛物线上方,且
的周长最小值为
.
的方程;
(2)点
是抛物线上的动点,点
是点
处抛物线切线的交点,若
的面积等于32,线段
为圆
的直径,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d945b17623cd01fa90180c4d4fca91f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b1a27a8413f67d9f97785d9889e4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131ebfee8d3fd5d0c4d3b20012e232f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374cdec65a41dc616f6f099551880d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c8a7fc100c019e54242d3c323aba8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e265ce107592c375b78007107a9c00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99e568a7823999b05efcf80dc83be2b.png)
您最近一年使用:0次
2023·全国·模拟预测
名校
解题方法
4 . 已知抛物线
的焦点为
上任意一点
到
的距离与到点
的距离之和的最小值为3.
(1)求抛物线
的标准方程.
(2)已知过点
且互相垂直的直线
与
分别交于点
与点
,线段
与
的中点分别为
.若直线
的斜率分别为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b92dbe7d01d47d6c2db1396180caf76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f579b73ca01978ec68e716f993bc3766.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f65dbed884e2248ec075655c684aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
您最近一年使用:0次
2023-11-20更新
|
1055次组卷
|
8卷引用:高考2024年普通高等学校招生全国统一考试?信息卷数学(一)
(已下线)高考2024年普通高等学校招生全国统一考试?信息卷数学(一)(已下线)2024年普通高等学校招生全国统一考试·信息卷文科数学(七)(已下线)2024年普通高等学校招生全国统一考试·信息卷理科数学(七)(已下线)专题10 圆锥曲线综合大题10种题型归类-【寒假分层作业】2024年高二数学寒假培优练(人教A版2019选择性必修第一册)陕西省西安中学2024届高三模拟考试(一)数学(理科)试题(已下线)热点7-4 抛物线及其应用(6题型+满分技巧+限时检测)(已下线)2024年高考数学全真模拟卷08(新题型地区专用)(已下线)重难点14 圆锥曲线必考压轴解答题全归类【十一大题型】(举一反三)(新高考专用)-1
解题方法
5 . 已知抛物线
:
焦点为
,
为
上的动点,
位于
的上方区域,且
的最小值为3.
(1)求
的方程;
(2)过点
作两条互相垂直的直线
和
,
交
于
,
两点,
交
于
,
两点,且
,
分别为线段
和
的中点.直线
是否恒过一个定点?若是,求出该定点坐标;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](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/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecb847136c8c31614aa429f0682ba10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1412b5b8b5aa721798c12482deb7ef25.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
![](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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
名校
解题方法
6 . 已知抛物线
的焦点为
为
上一动点,
为圆
上一动点,
的最小值为
.
(1)求
的方程;
(2)直线
交
于
两点,交
轴的正半轴于点
,点
与
关于原点
对称,且
,求证
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3331494c6e0b32c275c259a2e0cb3ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56afb8c84a2105d525b84b6862a5426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a58ff7a13f16152401ca349421cb3b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b2ddeb37779605287cef2747cfeaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4fdc034b4d20f15869d4c79b8161a0b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba03798acadc858f297ea1139c6a5cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4980ccc3dc8d16df52b761d7cad24e.png)
您最近一年使用:0次
2023-06-16更新
|
588次组卷
|
5卷引用:湖南省长沙市雅礼教育集团2022-2023学年高二下学期期中数学试题
湖南省长沙市雅礼教育集团2022-2023学年高二下学期期中数学试题四川省宜宾市叙州区第一中学校2022-2023学年高二下学期期末考试数学(文)试题四川省宜宾市叙州区第一中学校2022-2023学年高二下学期期末考试数学(理)试题(已下线)第24讲 抛物线的简单几何性质6种常见考法归类(2)(已下线)通关练17 抛物线8考点精练(3)
名校
解题方法
7 . 已知抛物线
的焦点为
,直线
,点
,
是抛物线
上的动点.
(1)求
的最小值及相应点
的坐标;
(2)点
到直线
距离的最小值及相应点
的坐标;
(3)直线
过点
与抛物线
交于
、
两点,交直线
于
点,若
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51cbe3cd6f5aa46b03bfdecac4e87354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385cd2fe95ca8875c9bbbb77a9fb7cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbcf0320d94734aedd3d4e2e31b9827.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/f26528737caa9027c36ebc6cf7bb9f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)点
![](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/ac047e91852b91af639feec23a9598b2.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ded3639be0739bb3531ec3bea7e02e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabd0aa8e651f4d0d647a080ffe8b704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次