名校
解题方法
1 . 已知点
,
,
中恰有两个点在抛物线
上.
(1)求
的标准方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若点
,
在
上,且
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5590337b3868db8523eeb7f448efcf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f0ee968f9a247871a54e505fbd111b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9158f21b372fd0390fab040ad65c586.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb2356a3833defed220ee1fa481aad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2024-03-29更新
|
880次组卷
|
2卷引用:山东省青岛市2023-2024学年高二上学期期末学业水平检测数学试题
2 . 过抛物线
的焦点
作直线
与抛物线交于
两点,且
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8269049ffbda5333600284ee5a12f674.png)
A.直线![]() |
B.直线![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.直线![]() ![]() ![]() |
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解题方法
3 . 已知抛物线
的焦点
到点
的距离为
,直线
经过点
,且与
交于点
(
位于第一象限),
为抛物线上
之间的一点,
为点
关于
轴的对称点,则下列说法正确的是( )
![](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/4e820a33f036a3f45975eea34630bc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
4 . 已知抛物线
,其焦点为
.
(1)
两点为抛物线
上的动点且满足
,直线
不垂直于
轴,求证:线段
的垂直平分线过定点
,并求出点
的坐标;
(2)已知椭圆
,圆
,过(1)中点
作斜率分别为
的直线
,且满足
,直线
交椭圆
于
两点,直线
交圆
于
两点,点
为
中点,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4428756f1088ce78ed97cbcea99775f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302aab606cd719baba3de2574ed69457.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875a860a39f84b8e72083c4956b6cf15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc5f7e05d956c36a2b75c9bc5e7a19f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ad174ec05373ce76b93130de6b3450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4cc51d393a94365f7008de5eae8879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42e9eac0fd00efb8da426b92feb37d4.png)
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名校
解题方法
5 . 已知抛物线
,点
和
为此抛物线的两个内接三角形(即三角形的三个顶点均在拋物线上),且均以点
为直角顶点,则直线
与直线
的交点坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb9603390e28948abd2e3cd96e1720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9123f019ba7acfe433e1003737388de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9e0d54d839e1a809a9617d073ac53a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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名校
解题方法
6 . 直线
交抛物线
于
、
两点,
是
上不与
、
重合的一个动点.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d0ccf8ec1d9159aa165794e06e7e2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.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/4aa0df7f1e45f9de29e802c7f19a4f64.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)
A.存在正实数![]() ![]() ![]() |
B.![]() ![]() ![]() ![]() ![]() |
C.作![]() ![]() ![]() ![]() |
D.对于任意的正实数![]() ![]() ![]() ![]() |
您最近一年使用:0次
7 . 已知过
轴正半轴上一点
的直线
:
交抛物线
:
于
,
两点,且
,证明点
为定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8521011867cb921af7d8cdd083d751be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](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/c81c49a3844da390e16a8b0038f06b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
8 . 已知
是抛物线
的焦点,
,
是该抛物线上的任意两点,则正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.若![]() ![]() ![]() ![]() |
B.若直线![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若直线![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-01-29更新
|
207次组卷
|
2卷引用:山西省朔州市怀仁市2023-2024学年高三上学期第二次教学质量调研数学试题
解题方法
9 . 已知点A,B关于坐标原点O对称,
,圆M过点A,B且与直线
相切,记圆心M的轨迹为曲线
.
(1)求曲线
的方程;
(2)过曲线
上的动点P作圆G:
的切线
,
,交曲线
于C,D两点,对任意的动点P,都有直线
与圆G相切,求t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236f52e04ddbd7253f44b97c4756ef9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ede20ce638de73ac52d3c58122fd7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)过曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3322a46c7a347f874eb72161c0183c.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/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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2024-01-27更新
|
190次组卷
|
2卷引用:湖南省永州市2023-2024学年高二上学期期末质量监测数学试题
名校
解题方法
10 . 已知抛物线
的焦点为F,且A,B,C三个不同的点均在
上.
(1)若直线AB的方程为
,且点F为
的重心,求p的值;
(2)设
,直线AB经过点
,直线BC的斜率为1,动点D在直线AC上,且
,求点D的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a9efe4c27ce894634c9e4c737b5fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(1)若直线AB的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ba50e25f0d2099dce13f113685d233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cda12642d59a5817e8990c43de20535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7711afeb265550ead8321ea2a24d5.png)
您最近一年使用:0次
2024-01-18更新
|
609次组卷
|
4卷引用:河北省邢台市部分重点高中2023-2024学年高二上学期1月期末数学试题