解题方法
1 . 已知三条直线
(
)分别与抛物线
交于点
、
,
为
轴上一定点,且
,记点
到直线
的距离为
,△
的面积为
.
(1)若直线
的倾斜角为
,且过抛物线
的焦点
,求直线
的方程;
(2)若
,且
,证明:直线
过定点;
(3)当
时,是否存在点
,使得
,
,
成等比数列,
,
,
也成等比数列?若存在,请求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88036e3c1badc0d0b3f9145cd52d1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79059a3366ed1b339ba1317ce8a1e7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146294fdb064581da7987fdca20ee912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc5c895153932c3e827a464664cef90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439e95540157803d4ac3cf61a49f50a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f1254f1ff64e7fc1918b84e75dceaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468edcfef1bcd7e74491a57a70c1bcb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50a4b1e4f8b1d044300df7ef8205c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb4be53c952d1edc5ecba3125c1111a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9bb415ebf91617fe843b83d0a140ea.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a251fb581ee87c54da42d43dc0f8fb68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7803037f78d54221e0bd45a2bff37c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.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/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d0252c1b2f7d2a84b5c985d19d547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
解题方法
2 . 已知抛物线
,
为E上一点,P到E的焦点F的距离为5.
(1)求E的标准方程;
(2)设O为坐标原点,A,B为抛物线E上异于P的两点,且满足
.
(ⅰ)判断直线
是否过定点,若过定点,求出定点的坐标;若不过定点,请说明理由;
(ⅱ)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4e5ecfd084f909f441631462d75e13.png)
(1)求E的标准方程;
(2)设O为坐标原点,A,B为抛物线E上异于P的两点,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
(ⅰ)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7dbc5f85292795579155dfd3baff0e.png)
您最近一年使用:0次
3 . 已知
为抛物线
的焦点,过点
的直线与抛物线
交于不同的两点
、
,满足
.
(1)求抛物线
的方程;
(2)过点
且斜率为
的直线与直线
交于点
,
,证明:直线
经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a436db19eb954d31075d5398f1b92ecd.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/9c474bbc60e05ba94322fbbd1f9d0bd9.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b0b31588840d3b05aace35519ef0c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
您最近一年使用:0次
4 . 设抛物线
的焦点为F,点
,过F的直线交C于M,N两点.当直线MD垂直于x轴时,
.
(1)①求C的方程;
②若M点在第一象限且
,求
;
(2)动直线l与抛物线C交于不同的两点A,B,P是抛物线上异于A,B的一点,记PA,PB的斜率分别为
,
,t为非零的常数.
从下面①②③中选取两个作为条件,证明另外一个成立:①P点坐标为
; ②
;③直线AB经过点
.(注:若选择不同的组合分别解答,则按第一个解答计分.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c0c95d8afec8d1eeb0ad168941b2f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d4a2a035d302744fed6f65daa4ac55.png)
(1)①求C的方程;
②若M点在第一象限且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5756243ad2106e49f868027ba7aaa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
(2)动直线l与抛物线C交于不同的两点A,B,P是抛物线上异于A,B的一点,记PA,PB的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
从下面①②③中选取两个作为条件,证明另外一个成立:①P点坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba0353cb9fcd190b32d7c6a0500810b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd86c1240021f054e98e846d4cf614f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5ffd6acc4a898d94a118373f56c41d.png)
您最近一年使用:0次
5 . 抛物线
的焦点为
,准线
交
轴于点
,点
为准线上异于
的一点,直线
上的两点
,
满足
(
为坐标原点),分别过
,
作
轴平行线交抛物线
于
,
两点,则( )
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5773ed04d47adbfbd5c810891b64e39b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.![]() | B.![]() |
C.直线![]() ![]() | D.五边形![]() ![]() |
您最近一年使用:0次
6 . 已知直线
与抛物线
相切于点A,动直线
与抛物线C交于不同两点M,N(M,N异于点A),且以MN为直径的圆过点A.
(1)求抛物线C的方程及点A的坐标;
(2)当点A到直线
的距离最大时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8a3365e99f926b1dafa901ab232152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求抛物线C的方程及点A的坐标;
(2)当点A到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-03-07更新
|
3667次组卷
|
5卷引用:山东省济宁市2023届高考一模数学试题
山东省济宁市2023届高考一模数学试题“七省联考”2024届高三考前猜想数学试题(已下线)考点15 直线与圆锥曲线相切问题 2024届高考数学考点总动员河南省商丘市虞城县第一高级中学2024届高三上学期第三次月考数学试题山东省济南市2023-2024学年高二上学期期末质量检测模拟数学试题
7 . 如图,已知
为抛物线
内一定点,过E作斜率分别为
,
的两条直线,与抛物线交于
,且
分别是线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/3f33f3e8-6c69-48ef-ac2c-d174c48546af.png?resizew=213)
(1)若
且
时,求
面积的最小值;
(2)若
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dbd8408efb06329ffa9841a9e37edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.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/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/3f33f3e8-6c69-48ef-ac2c-d174c48546af.png?resizew=213)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4cc51d393a94365f7008de5eae8879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48e42ce4fd7e6da946bf2b7b22200db.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07a58b07585c8a48a6c552e0063686a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2023-03-01更新
|
2406次组卷
|
5卷引用:广东省汕头市2023届高三第一次模拟数学试题
广东省汕头市2023届高三第一次模拟数学试题(已下线)广东省汕头市2023届高三第一次模拟数学试题变式题17-22(已下线)3.3.2 抛物线的简单的几何性质(重难点突破)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)2024届高三新高考改革数学适应性练习(一)(九省联考题型)(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