名校
解题方法
1 . 过双曲线
的左焦点
作圆
的切线,切点为
.直线
交抛物线
于点
,若
(
为坐标原点),则双曲线的离心率为_____________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0944c99f34ee41bea845303ed15a7d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4be819fc47b2aa19ab2022b3dfeb6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2273ae1ee99cec9c1304323bc9ebf75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae6433125ae380b1ba0c41a146ab004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd25ffc875fbbe495c1aaf7f5673133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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2 . 在平面直角坐标系中,若
的坐标
,
满足方程
,则点
的轨迹是__________ (填曲线的类型,填方程不给分).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5f443cc1db0eb6ad3975ddb1a9fc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
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2024-02-14更新
|
244次组卷
|
3卷引用:河南省济源市2023-2024学年高二上学期期末质量调研数学试题
河南省济源市2023-2024学年高二上学期期末质量调研数学试题(已下线)2.5 曲线与方程(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)上海市扬子中学2023-2024学年高一下学期期中考试数学试题
解题方法
3 . 在平面直角坐标系
中,已知点
,记抛物线
:
上的动点
到准线的距离为
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f54dd475ff1321041c80738b201c3b6.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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117c99311ee75f265efbbbca77812a52.png)
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名校
4 . 已知抛物线
的焦点为
,准线为
,点
在抛物线
上,过
作
的垂线,垂足为
,若
(
为坐标原点),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd29b2e8192d673308bdf8d5cb6cab.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.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/bfa2c333eb3a718785c053a900c10d9a.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e430de9d088494fae303e65baf93a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd29b2e8192d673308bdf8d5cb6cab.png)
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2024-02-12更新
|
125次组卷
|
2卷引用:广东省高州市2023-2024学年高二上学期期末教学质量监测数学试题
解题方法
5 . 已知抛物线
上一点
,则点
到该抛物线的焦点
的距离为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7585c7944d095b903c6e0d3dcbc228e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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解题方法
6 . 抛物线
上一点
到焦点
的距离为2,则延长
交抛物线于点
,则
的值为___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.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/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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解题方法
7 . 已知
,
,
是抛物线C:
上的一点,则
周长的最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab47bf43b2c5d6395129b80ddfbb1b24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef03f452410ab19c6246567c427178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3577bf250e9110428ff34f518fbd9f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
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2024-02-11更新
|
157次组卷
|
2卷引用:河北省保定市定州市2023-2024学年高二上学期1月期末考试数学试题
解题方法
8 . 圆锥曲线因其特殊的形状而存在着特殊的光学性质.我们知道,抛物线的光学性质是平行于抛物线对称轴的光线经抛物线反射后汇聚于其焦点;双曲线的光学性质是从双曲线一个焦点发出的光,经过双曲线反射后,反射光线的反向延长线都汇聚到双曲线的另一个焦点上.卡式望远镜就是应用这些性质设计的.下图为卡式望远镜的中心截面示意图,其主要由两块反射镜组成,主镜是中央开孔的凹抛物面镜
,副镜是双曲线左支的旋转面型凸双曲面镜
,主镜对应抛物线的顶点与副镜对应双曲线的中心重合,当平行光线投射到主镜上时,经过主镜反射,将汇聚到主镜的焦点
处,但光线尚未汇聚时,又受到以
为焦点的凸双曲面镜的反射,穿过主镜中心的开孔后汇聚于另一个焦点
处.以
的中点为原点,
为
轴,建立平面直角坐标系.若
米,凹抛物面镜的口径
为
米,凸双曲面镜的口径
为1米,要使副镜的反射光线全部通过凹抛物面镜
的中央孔洞,则孔洞直径最小为___________ 米.
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621f16b930274bf27e1a7fe00a1f0f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b4dead9413f96719f08807ef721d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/7/93e98f43-64f8-4671-8aab-f68559e8286f.png?resizew=181)
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9 . 已知正方体
的棱长为2,E为棱
的中点,F,Q分别是线段
上的两个动点,
为正方体表面
上一点,若
到棱
与到棱
的距离相等,则
的最小值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5081ee229e252b7812f0b7771d7d3baf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6288233eaba9ae91e2c3683eb1c6c3d.png)
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