解题方法
1 . 已知点
在抛物线
的准线上,记抛物线C的焦点为F,则以原点为圆心,且与直线AF相切的圆的半径为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acf45a5f66394502b70bf1dd68ee40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
A.![]() | B.2 | C.![]() | D.5 |
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3卷引用:2019届云南省曲靖市高中毕业生(第二次)复习统一检测理科数学试题
名校
解题方法
2 . 已知抛物线
,点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfb23a9e07213cb76990dbedfc7feca.png)
(1)求点
与抛物线
的焦点
的距离;
(2)设斜率为
的直线
与抛物线
交于
两点,若
的面积为
,求直线
的方程;
(3)是否存在定圆
,使得过曲线
上任意一点
作圆
的两条切线,与曲线
交于另外两点
时,总有直线
也与圆
相切?若存在,求出
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfb23a9e07213cb76990dbedfc7feca.png)
(1)求点
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
(2)设斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)是否存在定圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcecc757a9b708d12ea6349475029d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2020-01-13更新
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5卷引用:上海市建平中学2020届高三上学期12月月考数学试题
上海市建平中学2020届高三上学期12月月考数学试题上海市浦东新区建平中学2018-2019学年高三下学期3月月考数学试题2017年上海市建平中学高三三模数学试题(已下线)黄金卷12-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(新高考专用)湖南省长沙市雅礼中学2021届高三下学期月考(八)数学试题
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3 . 抛物线
的焦点坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2019-10-20更新
|
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9卷引用:四川省攀枝花市2018-2019学年高二下学期期末数学试题
四川省攀枝花市2018-2019学年高二下学期期末数学试题吉林省长春市实验中学2019-2020学年高二上学期10月月考数学(文)试题(已下线)2019年11月10日《每日一题》一轮复习数学(文)- 每周一测江苏省镇江中学2019-2020学年高二上学期第一次月考数学试题江苏省镇江中学2019-2020学年高二上学期10月月考数学试题2015-2016学年浙江省杭州市七校高二下期中数学试卷甘肃省金昌市永昌县第一高级中学2020-2021学年高二下学期期中数学(文)试题陕西省宝鸡市眉县中学2022-2023学年高二下学期第一次月考文科数学试题江苏省徐州市铜山区2023-2024学年高二上学期学情调研数学试卷
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4 . 已知抛物线y=ax2过点(4,2),则a=_____ ,准线方程为_____
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3卷引用:浙江省温州十五校联合体2018-2019学年高二下学期期末联考数学试题
浙江省温州十五校联合体2018-2019学年高二下学期期末联考数学试题(已下线)专题3.3抛物线(A卷基础篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教A版,浙江专用)天津市滨海新区塘沽第一中学2022-2023学年高二上学期期中数学试题
5 . 已知抛物线
上一点
到焦点F的距离
,倾斜角为α的直线经过焦点F,且与抛物线交于两点A、B.
(1)求抛物线的标准方程及准线方程;
(2)若α为锐角,作线段AB的中垂线m交x轴于点P.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eda0d8732b07b06693bde233fb208c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3294a1b0769d2936880580b991b870a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90e4d97e31ea11615f23e53c285b319.png)
(1)求抛物线的标准方程及准线方程;
(2)若α为锐角,作线段AB的中垂线m交x轴于点P.证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3a52a11565502a8d918d493604f425.png)
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6 . 已知抛物线
上一点
到焦点
的距离
,倾斜角为
的直线经过焦点
,且与抛物线交于两点
、
.
(1)求抛物线的标准方程及准线方程;
(2)若
为锐角,作线段
的中垂线
交
轴于点
.证明:
为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ddd8188218c214b934c35564f87673c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e9e89f5ece16db5cf7c5f4fdc56ec1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671b66ae9432d2220c49e5d1da9a6984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求抛物线的标准方程及准线方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/285a703081e781113a77f3b221011a72.png)
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2019-09-13更新
|
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4卷引用:【全国市级联考 】四川省内江市2018-2019学年高二下学期期末检测数学(理)试题
解题方法
7 . 已知点A是抛物线
的对称轴与准线的交点,点B为抛物线的焦点,P在抛物线上且满足
,当
取最大值时,点P恰好在以
、
为焦点的双曲线上,则双曲线的离心率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bcdcd019945933d20cc6e90af7eb92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
8 . 已知抛物线
(
),点
在
的焦点
的右侧,且
到
的准线的距离是
到
距离的3倍,经过点
的直线与抛物线
交于不同的
、
两点,直线
与直线
交于点
,经过点
且与直线
垂直的直线
交
轴于点
.
(1)求抛物线
的方程和
的坐标;
(2)判断直线
与直线
的位置关系,并说明理由;
(3)椭圆
的两焦点为
、
,在椭圆
外的抛物线
上取一点
,若
、
的斜率分别为
、
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca3be22daa1081710f6c8a39bb44750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47968de4a67d1083d36c173b3d3c2ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf0685aa2108c61b1e8ab48d3d7c4bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/ae7a3e520a16d4fdd73c4e6a4ce7be0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d2b01f86fb5a373af6b089cf3d891b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7a3e520a16d4fdd73c4e6a4ce7be0e.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/acc290b44635265137fdf13146b6a6d9.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
(3)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623567de59e50e4066c20804e9168ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09a8ac969e5cec3be6abf4ff44c692e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623567de59e50e4066c20804e9168ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c139977cac26d9dd6acabec625206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2491acadeba63c5df0b87f7326841376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f375dc5addedc5f9fbb72d566939c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731f980ccb6f902d460d0ea2920bfe2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae28d162338771867dc6805f9dc9dfd6.png)
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9 . 若角
终边上的点
在抛物线
的准线上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a18798408a1b91fdb12deb79f0b562a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3adf2aa8b62c1fddb25377e642e2dc2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ed2787d17f6807fe7b3c269ee669d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a18798408a1b91fdb12deb79f0b562a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-06-18更新
|
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8卷引用:【市级联考】河北省廊坊市2018-2019学年高二第二学期期中联合调研考试理科数学试题
名校
10 . 已知函数
在区间
上的最大值为
,则抛物线
的准线方程是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4faed370c702ab378e577ff44be176c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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3卷引用:【校级联考】河南省名校2018-2019学年高二5月联考数学(文科)试题