名校
解题方法
1 . 已知抛物线C:
的焦点为F,P为抛物线C上一动点,点Q为线段PF的中点.
(1)求点Q的轨迹方程;
(2)求点Q的轨迹与双曲线
的交点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
(1)求点Q的轨迹方程;
(2)求点Q的轨迹与双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4334e343daae170f14d086661bc5792a.png)
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2022-12-12更新
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3卷引用:吉林省四平市第一高级中学2021-2022学年高二上学期第三次月考数学试题
解题方法
2 . 已知抛物线C:y2=4x.
(1)若C与圆G:(x﹣4)2+y2=13在第一象限内交于M,N两点,求直线MN的方程;
(2)直线l过点D(﹣1,0)交C于A,B两点,点B关于x轴的对称点为E,直线AE交x轴于点P,求证:P为定点.
(1)若C与圆G:(x﹣4)2+y2=13在第一象限内交于M,N两点,求直线MN的方程;
(2)直线l过点D(﹣1,0)交C于A,B两点,点B关于x轴的对称点为E,直线AE交x轴于点P,求证:P为定点.
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2022-04-07更新
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5卷引用:山东省2021年普通高等学校招生全国统一考试模拟数学试题
山东省2021年普通高等学校招生全国统一考试模拟数学试题山东省泰安市2021届高三四模数学试题(已下线)专题15 圆锥曲线常考题型03——定点问题-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)(已下线)专题3.16 圆锥曲线中的定点、定值问题大题专项训练(30道)-2021-2022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)陕西省渭南市澄城县2023-2024学年高二上学期期中文化课检测数学试题
3 . 若曲线T:
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7885f39a8de2b188187691b3b316b5d9.png)
A.若A=C,B=0,则T是圆 |
B.若A>C>0,B=D=E=0,F<0,则T是长轴长为![]() |
C.若A>0,C<0,B=D=E=0,F<0,则T是离心率为![]() |
D.若A=1,B=-1,C=D=E=0,F=1,则T与直线![]() |
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名校
解题方法
4 . 抛物线
与圆
交于
、
两点,圆心
,点
为劣弧
上不同于
、
的一个动点,平行于
轴的直线
交抛物线于点
,则
的周长的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84107fc934c3519b7f9c0121506801c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211401fa5e6f95cb23d1f06e80c90108.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/b6b0fc22034c9db29b23c4cf9faf5af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d372c99450c4fbbbb0f397e5ecb82c.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2022-01-21更新
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384次组卷
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2卷引用:山东省菏泽市菏泽第一中学2021-2022学年高二上学期期中数学试题
5 . 在平面直角坐标系中,已知曲线
上任意点
与两个定点
和点
连线的斜率之和等于
,曲线
上任意点
与两个定点
和点
连线的斜率之积等于
,则关于曲线
、
的结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
A.曲线![]() |
B.曲线![]() ![]() |
C.曲线![]() ![]() |
D.过![]() ![]() ![]() |
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6 . 关于曲线
的下列说法,其中正确的序号是___________ .
①关于原点对称;
②是封闭图形,面积大于
;
③不是封闭图形,与圆
无公共点;
④与曲线
的四个交点恰为正方形的四个顶点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66eda389249f92eaba886f7c67e05e89.png)
①关于原点对称;
②是封闭图形,面积大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
③不是封闭图形,与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
④与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f831661fc06b97d143f8e35710c7883c.png)
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名校
7 . 已知曲线
,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66eda389249f92eaba886f7c67e05e89.png)
A.曲线C关于原点对称 |
B.曲线C是封闭图形,且封闭图形的面积大于![]() |
C.曲线C不是封闭图形 |
D.曲线C与圆![]() |
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名校
8 . 已知心形线是由一个圆上的一个定点,当该圆绕着与其相切且半径相同的另外一个圆周上滚动时,这个定点的轨迹,因为其形状像心的形状而得名.在极坐标系
中,方程
表示的曲线
就是一条心形线,如图,以极轴
所在直线为
轴,极点
为坐标原点的直角坐标系
中,已知曲线
的参数方程为
(
为参数).
![](https://img.xkw.com/dksih/QBM/2021/11/8/2846752386367488/2850540072157184/STEM/2be71326-2d9a-4f3a-84fa-cbfce7132cdc.png)
(1)求曲线
的极坐标方程;
(2)求曲线
与
交点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c32c6873c5c65beed9a5ab160e14230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b948d7f23155a7d3c9d23c710f227add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/2021/11/8/2846752386367488/2850540072157184/STEM/2be71326-2d9a-4f3a-84fa-cbfce7132cdc.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2021-11-13更新
|
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|
3卷引用:江西省九江市柴桑区第一中学2022届高三上学期第二次月考数学(理)试题
名校
解题方法
9 . 已知圆
与抛物线
相交于点
,
,
,
,且在四边形
中,
.
![](https://img.xkw.com/dksih/QBM/2021/11/11/2848908578332672/2849264380796928/STEM/67a86025e398470c9902f7c282e47d69.png?resizew=227)
(1)若
,求实数
的值;
(2)设
与
相交于点
,
与
组成蝶形的面积为
,求点
的坐标及
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519d5dfc27226492c7003c73534624bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb9757015d815d02e8e99f2475ce3e3.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://img.xkw.com/dksih/QBM/2021/11/11/2848908578332672/2849264380796928/STEM/67a86025e398470c9902f7c282e47d69.png?resizew=227)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2697bd158b528c992421d24cd7813c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef4b54df90e5528f155ab2902a2eea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffffbccf0eb96123a237860c12a1b892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2021-11-11更新
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4卷引用:江苏省泰州中学2021-2022学年高二上学期期中数学试题
10 . 已知
,
与x轴交点为A,若对于
图像上任意一点P,在其图像上总存在另一点Q(P、Q异于A),满足
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c930ab1239f1e842d6a448c255be76bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e8b17a7840ae7b75590da92fa0965b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33091c6dcc5e3c822fa3242c9437aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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