名校
解题方法
1 . 已知抛物线
的焦点为
,准线
与抛物线
的对称轴的交点为
,点
在抛物线
上,且
.
(1)求抛物线
的方程;
(2)若直线
交抛物线
于
两点,点A在
轴上的投影为
,直线
分别与直线
(
为坐标原点)交于点
,与直线
交于点
,记
的面积为
,
的面积为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697e630cc74997bb70d1ac52ac6f5b8f.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/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a613a78fce2408a3747d756adec7ed9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4813313efdc0c47fb6ef1b3a00ecff.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7164d82a29a81b365d7a17af0430502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39dbc32b4a090860784dca8541218a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b5cc7218f5ce4a562eb5131d6b85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532d9de08698f61d7c010805c61a4ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dd78e9156dcf6db93f6cbcc5b43b14.png)
您最近一年使用:0次
解题方法
2 . 已知抛物线
的焦点为
,直线
与抛物线
交于点
,且
.
(1)求抛物线
的方程;
(2)直线
与C交于A,B两点,点T在y轴上,直线
,
与C的另一个交点分别为D,E,且
,求T点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971751ce826c71fb6ec79969d45a9fdc.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/5b59fa819dda388090534b06bccee422.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c966320d637cab491c67425ef1338966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98c4b3f3fe826e124ca7d199d4ca4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817a419430d9951cbdb89b657b21bcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0aa4c793921fdaa5d430cb90d78ca6.png)
您最近一年使用:0次
2022-05-18更新
|
408次组卷
|
4卷引用:河南省焦作市2022届高三下学期第三次模拟考试文科数学试题
2022·全国·模拟预测
解题方法
3 . 已知抛物线
与双曲线
有相同的焦点,且它们的一个交点为
.
(1)求抛物线
的标准方程.
(2)设点
,
,若过
的直线与抛物线
交于不同的两点
,
,且直线
与抛物线
交于点
(不同于点
),问直线
是否经过定点?若经过,求出定点坐标;若不经过,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd154f66ff709db10e765f6b3a728be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f88b7ecc9ce449b5ab52aefeea91735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b8784db33d2167f3d8ddb508787d0a.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c87b7e39ab4c173e357d92f345ddab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8efe0cd08f051818b21f7bca7f1183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.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/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
您最近一年使用:0次
2022·全国·模拟预测
4 . 已知
为坐标原点,抛物线
的方程为
,
的焦点为
,直线
与
交于
,
两点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2022-05-17更新
|
1670次组卷
|
9卷引用:2022年高考最后一卷(押题卷八)数学试题
(已下线)2022年高考最后一卷(押题卷八)数学试题福建省厦门外国语学校2021-2022学年高二下学期数学期末模拟试题(2)(已下线)重难点14三种抛物线解题方法-1(已下线)3.3.2 抛物线的几何性质(难点)-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)山东省济南市2022届高三二模数学试题变式题11-16湖南省长沙市望城区第一中学2022-2023学年高二下学期期末模拟数学试题(已下线)第13讲 抛物线(9大考点)(2)河北省邯郸市魏县第五中学2022-2023学年高二上学期期末数学试题(已下线)第七节 抛物线 第二课时 直线与抛物线的位置关系 讲
2022·全国·模拟预测
解题方法
5 . 在平面直角坐标系xOy中,抛物线C:
上一点
到焦点F的距离为5.
(1)求抛物线C的标准方程;
(2)若直线l:
交抛物线C于A,B两点,且点
,求△ABN面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bdf9e8ef162d7d905b02b9a5dd8a4f3.png)
(1)求抛物线C的标准方程;
(2)若直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/405de5086d88fa0a2e66e122ba669e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0a807a550b61acd46aa4f8677dd6d3.png)
您最近一年使用:0次
6 . 如图,已知抛物线
和点
,点P到抛物线C的准线的距离为6.
![](https://img.xkw.com/dksih/QBM/2022/5/17/2981204673331200/2981246892580864/STEM/5ce2cec9-f3ee-4b17-b4e6-479edf30afd6.png?resizew=352)
(1)求抛物线C的标准方程;
(2)过点P作直线
交抛物线C于A,B两点,M为线段
的中点,点Q为抛物线C上的一点且始终满足
,过点Q作直线
交抛物线C于另一点D,N为线段
的中点,F为抛物线C的焦点,记
的面积为
,
的面积为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1991b5dc6ebe1f9ed37c1a97966aabf4.png)
![](https://img.xkw.com/dksih/QBM/2022/5/17/2981204673331200/2981246892580864/STEM/5ce2cec9-f3ee-4b17-b4e6-479edf30afd6.png?resizew=352)
(1)求抛物线C的标准方程;
(2)过点P作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6163721b2a24d30c0d338969de0c0670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a23dff476ddce008f686a26be4adbef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c118858379800688c993a8b61270b356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e1de0c6dca3c0d5c9207abe780d457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c3b743769d19231c2165ec275bab1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c21cbb1c2bcbcb8391ac5a879f2ae0.png)
您最近一年使用:0次
解题方法
7 . 已知抛物线
,点
在E上.
(1)求E的方程;
(2)设动直线l交E于A,B两点,点P,Q在E上,且
,若直线l始终平分弦PQ,求点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814e6905cbde780e189ad164792fe0db.png)
(1)求E的方程;
(2)设动直线l交E于A,B两点,点P,Q在E上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9b9bb0f509e6f3d30858efb217c1f5.png)
您最近一年使用:0次
8 . 如图,已知抛物线
上有一动点
,M为y轴上的动点,设
,连接
与
交于点B,过B作
的切线交
的延长线于点H,连接
交C于点E,连接
交y轴于点G,分别记
的面积为
.
![](https://img.xkw.com/dksih/QBM/2022/5/15/2979791034212352/2979995582226432/STEM/2a759791-3864-4501-af6a-c5c64da8aace.png?resizew=273)
(1)若
,求p;
(2)若
,求证:
是
之间的一个定值(不必求出定值).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633ad134a0b478865331a4d50765ea39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfb2a536197b222df8b10a4c453f05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca26e29d00ff4ce2345d77e7d8f07b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83042953e7f15e984b2da2ee9ca678d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a1d4c4b3c645336020f25debd656c1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://img.xkw.com/dksih/QBM/2022/5/15/2979791034212352/2979995582226432/STEM/2a759791-3864-4501-af6a-c5c64da8aace.png?resizew=273)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bbb711b435935e64e1242f5b0de039d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a46d75a74e148cb708d400f018875c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf277d377c0f1ad6e23b8a7ed0da6c4.png)
您最近一年使用:0次
名校
9 . 已知抛物线
,点
为抛物线上一点,F为抛物线的焦点,且
.
(1)求抛物线的方程;
(2)过焦点F的直线l与抛物线交于A、B两点,点P为抛物线上异于A、B的任意一点,直线
、
分别与抛物线的准线相交于D、E两点,证明:以线段
为直径的圆经过y轴上的两个定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097f0bb97579029799b799de78b740fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c382973a38078f05972fbbb5a6a3aa54.png)
(1)求抛物线的方程;
(2)过焦点F的直线l与抛物线交于A、B两点,点P为抛物线上异于A、B的任意一点,直线
![](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/e6e490f703eb6c9bb1278c78ebc2d661.png)
您最近一年使用:0次
2022-05-15更新
|
611次组卷
|
2卷引用:江西省重点中学协作体2022届高三下学期第二次联考数学(文)试题
名校
解题方法
10 . 已知抛物线C:
,F为抛物线C的焦点,
是抛物线C上点,且
;
(1)求抛物线C的方程;
(2)过平面上一动点
作抛物线C的两条切线PA,PB(其中A,B为切点),求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2040b8fae7f5af94b0d911ab6255da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532bcbe8307e6b2129bdcdbd553ee5f3.png)
(1)求抛物线C的方程;
(2)过平面上一动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864a1045399e9970fe9684e9644dc061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e5109b55b3b96af00c792527c77cca.png)
您最近一年使用:0次
2022-05-15更新
|
1313次组卷
|
8卷引用:江西省(东乡一中、都昌一中、丰城中学、赣州中学、景德镇二中、上饶中学、上栗中学、新建二中)新八校2022届高三下学期第二次联考数学(文)试题
江西省(东乡一中、都昌一中、丰城中学、赣州中学、景德镇二中、上饶中学、上栗中学、新建二中)新八校2022届高三下学期第二次联考数学(文)试题(已下线)2022年全国高考甲卷数学(文)试题变式题13-16题(已下线)2022年全国高考甲卷数学(文)试题变式题21-23题湖北省荆州中学2022-2023学年高二上学期期末数学试题(已下线)模块八 专题9 以解析几何为背景的压轴解答题(已下线)专题3.7 直线与抛物线的位置关系【八大题型】-2023-2024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)2023-2024学年高二上学期期末数学仿真模拟试题02(新高考地区专用)2023-2024学年高二上学期期末仿真模拟数学试题05(新高考地区专用)