解题方法
1 . 曲线
,第一象限内点A在Γ上,A的纵坐标是a.
(1)若A到准线距离为3,求a;
(2)若a=4,B在x轴上,AB中点在F上,求点B坐标和坐标原点O到AB距离;
(3)直线
,令P是第一象限Γ上异于A的一点,直线PA交l于Q,H是P在l上的投影,若点A满足“对于任意P都有
”,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32e577ae1f4449efbd64c1199efe7a3.png)
(1)若A到准线距离为3,求a;
(2)若a=4,B在x轴上,AB中点在F上,求点B坐标和坐标原点O到AB距离;
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0778559e1601f19625786dc20304fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c881d2c8b04768a6820995f1c8c209dd.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,已知抛物线
在点
处的切线
与椭圆
相交,过点
作
的垂线交抛物线
于另一点
,直线
(
为直角坐标原点)与
相交于点
,记
、
,且
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712433026957312/2714531731161088/STEM/b67f6c8f-4fc3-4a5b-9f8a-c09d4ce19dc0.png?resizew=203)
(1)求
的最小值;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4428756f1088ce78ed97cbcea99775f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9724fd240c60553bffc050d502e9a18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/6270bb08b90f72d5671ab8225f356c43.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712433026957312/2714531731161088/STEM/b67f6c8f-4fc3-4a5b-9f8a-c09d4ce19dc0.png?resizew=203)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e86e6f0ac5903369afea2c8d04ba412.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fc44bdd2913504cd806ecbe56fc9fd.png)
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2021-05-05更新
|
1438次组卷
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6卷引用:浙江省杭州市2021届高三下学期4月二模数学试题
浙江省杭州市2021届高三下学期4月二模数学试题(已下线)【新东方】高中数学20210429—009【2021】【高三下】(已下线)专题11.平面解析几何(解答题)-《2022届复习必备-2021届浙江省高考冲刺数学试卷分项解析》山东省日照市2023届高三下学期4月校际联合考试数学试题广东省深圳市福田区红岭中学2023届高三第五次统一考数学试题辽宁省辽宁师范大学附属中学2023年高三下学期5月月考数学试题
名校
解题方法
3 . 已知
,曲线
、
的方程分别为
和
,
与
在第一象限内相交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/d6a3207c-a7b3-478f-b066-21e25fb30664.png?resizew=179)
(1)若
,求
的值;
(2)若
,定点
的坐标为
,动点
在直线
上,动点
在曲线
上,求
的最小值;
(3)已知点
、
在曲线
上,点
、
关于直线
的对称点分别为
、
,设
的最大值为
,
的最大值为
,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dece47c23e53eca430269ad7b12e0891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2216525c2e569d608eaa59779d4b7c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f5a9867a4462961a98c1e5c5e00b9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca072cc62e09a771423ae1f4ceea5ba5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/d6a3207c-a7b3-478f-b066-21e25fb30664.png?resizew=179)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee4f1435f083b29366171c5f2d9334e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfa2a6d9749a619edf80bad8b3e4962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6115df2ed89b37d9fe8a92faf7f73d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7593498eac4b57dbd2a07d941812867d.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069bfae6fbefdb44878357b98789e5a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f126ffed44c65c7d4afd081776ed35d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.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/d77f5191798242b7b9b88a75e17e4425.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/21448de9fe4710bf0d48138724832031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60436c1f7b5c2f6b5331548216e8077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f404e301cf47816f0698d4ac194ffb37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2023-12-12更新
|
411次组卷
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3卷引用:上海市闵行区2024届高三上学期学业质量调研(一模)数学试卷
4 . 第一象限的点
在抛物线
上,过点
作
轴于点
,点
为
中点.
(1)求
的运动轨迹曲线
的方程;
(2)记
的焦点分别为
,则四边形
的面积是否有最值?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78085edbc651832e493d037594d205b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d0b82d9c9b2e6de5141b0a82e42c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78085edbc651832e493d037594d205b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f420670a58330f3377c5906af03e305c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da5b8b7647e3f1ebbc8af579580c25cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636f81dbf897fe18e90a962964f0f699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fbde43cf56c148c48e1a2a3fc1670f2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636f81dbf897fe18e90a962964f0f699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62cde0eb1accdc00d575fd291fb07673.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a42d1b8468f34296491ba478adc7ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1daf054dfdaba105b7d0029da94c4bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c36aa002197f891acc1132c887871ce.png)
您最近一年使用:0次
5 . 如图,已知椭圆
和抛物线
,斜率为正的直线
与
轴及椭圆
依次交于
、
、
三点,且线段
的中点
在抛物线
上.
![](https://img.xkw.com/dksih/QBM/2022/2/1/2907029768708096/2916957964623872/STEM/72e944f44b3a4ec3ac4c463746502027.png?resizew=212)
(1)求点
的纵坐标的取值范围;
(2)设
是抛物线
上一点,且位于椭圆
的左上方,求点
的横坐标的取值范围,使得
的面积存在最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4338a6909974a73a11b38df333a740db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5251f627988fa20bd12c6a63e2cf969f.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/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://img.xkw.com/dksih/QBM/2022/2/1/2907029768708096/2916957964623872/STEM/72e944f44b3a4ec3ac4c463746502027.png?resizew=212)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
您最近一年使用:0次
6 . 如图,已知点
是焦点为
的抛物线
上一点,
,
是抛物线
上异于
的两点,且直线
,
的倾斜角互补,若直线
的斜率为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/f44866ad-a43b-4257-ab0a-160e1c27ea00.png?resizew=154)
(Ⅰ)证明:直线
的斜率为定值;
(Ⅱ)求焦点
到直线
的距离
(用
表示);
(Ⅲ)在
中,记
,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2007972af3341f27fbc32ce62dfce5e2.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2781714853ddd3675560abfaa967242.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/f44866ad-a43b-4257-ab0a-160e1c27ea00.png?resizew=154)
(Ⅰ)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(Ⅱ)求焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(Ⅲ)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7cd0e6d684f1983034c305af2f24cc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06433d26939d333c62823d6113f98177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94ff61f05b1a88f9f9f785441bfcc92.png)
您最近一年使用:0次
解题方法
7 . 已知点
,
、
两点分别在
轴、
轴上运动,且满足
,
.
(1)求
的轨迹方程;
(2)若一正方形的三个顶点在点
的轨迹上,求其面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d698fc64e796043e7a1c97ecf8aad1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21959efd16e1cd04628ae18d6351f125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a9c252a1da924943190e0d197b330c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4444f6082876c1d0556e482d27782e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82359cd0c03ac3b86e8dd8845598a0a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b398d115be8eb3de8fb1ad1c1dd7fec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd6065c5f02b77c719ead43ab718b89.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bdb70612c69e2ae9d8b07f989468b3.png)
(2)若一正方形的三个顶点在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bdb70612c69e2ae9d8b07f989468b3.png)
您最近一年使用:0次
名校
解题方法
8 . 直线
与抛物线
相交于
,
两点,过
,
两点分别作该抛物线的切线,与直线
均交于点
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b26dff558266a554cbf182a7b4ef42f.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc3c79b72ecd228354b0a8ec40959957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.直线![]() ![]() |
B.![]() ![]() ![]() |
C.存在某一条直线![]() ![]() |
D.设点![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
9 . 抛物线
的焦点为F,准线为
是抛物线上一点,过F的直线交抛物线于A,B两点,直线AP、BP分别交准线
于M、N.当
,点P恰好与原点O重合时,
的面积为4.
![](https://img.xkw.com/dksih/QBM/2021/5/22/2726676338499584/2732237003841536/STEM/b716c866-c9f1-4356-8cc5-d73456cb7a6f.png?resizew=205)
(1)求抛物线C的方程;
(2)记
点的横坐标与AB中点的横坐标相等,若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ea803e31d2dedcf0590e0a0475e7ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cc699a65e140dd4be6195f25c1e85d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33181b27b10690b4913595f8c1f46e.png)
![](https://img.xkw.com/dksih/QBM/2021/5/22/2726676338499584/2732237003841536/STEM/b716c866-c9f1-4356-8cc5-d73456cb7a6f.png?resizew=205)
(1)求抛物线C的方程;
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe0bc8a9436bb738559b4aff7d4c721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8278a07eacf95a307186ba96fcb7b164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
解题方法
10 . 设圆D:
与抛物线C:
交于E,F两点,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb7aad3f2957f8beb69665aa1c60919.png)
(1)求抛物线C的方程;
(2)若直线l:
与抛物线C交于A,B两点
点A在第一象限
,动点
异于点A,
在抛物线C上,连接MB,过点A作
交抛物线C于点N,设直线AM与直线BN交于点P,当点P在直线l的左边时,求:
①点P的轨迹方程;
②
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5a589fdbfd61132f773e457a221797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb7aad3f2957f8beb69665aa1c60919.png)
(1)求抛物线C的方程;
(2)若直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb403a333c9e8fd9a3e7c100fb6017b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b554486bc34b098b4b3e878a2c4613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca51d433190304dd9811b0a1f7b4beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c51b7b9dcf8c1b17609ae6999e46f6f.png)
①点P的轨迹方程;
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
您最近一年使用:0次