名校
解题方法
1 . 如图,过抛物线
的焦点
作直线,与抛物线及其准线分别交于
,
,
三点,若
,则直线
的方程__________ ,
的面积是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6824930af2753388d21fb88506a2dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/846faa2b-12a1-4eff-94b3-fa4a16530216.png?resizew=144)
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名校
解题方法
2 . 斜率为
的直线经过抛物线
的焦点,且与抛物线交于A、B两点,则线段
的长为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2023-03-05更新
|
244次组卷
|
2卷引用:广东省珠海市第一中学2022-2023学年高二下学期3月月考数学试题
解题方法
3 . 希腊著名数学家阿波罗尼斯与欧几里得、阿基米德齐名.他发现:“平面内到两个定点
的距离之比为定值
的点的轨迹是圆”.后来,人们将这个圆以他的名字命名,称为阿波罗尼斯圆,简称阿氏圆.已知在平面直角坐标系
中,
,
,点
是满足
的阿氏圆上的任一点,则该阿氏圆的方程为____ ;若点
为抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdc384aa20e27b9289497e741e35554.png)
上的动点,
在
轴上的射影为
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a08f5d6f91366da27e9b96452bb04977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d4ad2f121598b00fdc0c7df7624f00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdc384aa20e27b9289497e741e35554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd6f651fa3d9aee69498289bb8702ff3.png)
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4 . 已知抛物线
的准线方程为
,若
上有一点
位于第一象限,且点
到抛物线焦点的距离为
,则点
的坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c98a7f3a8bf384b1dfc1d34aebd46d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2022-04-29更新
|
589次组卷
|
3卷引用:广东省佛山市南海区桂华中学2022届高三下学期第三次大测数学试题
名校
解题方法
5 . 已知
、
分别是双曲线
的左、右焦点,
也是抛物线
的焦点,点
是双曲线
与抛物线
的一个公共点,若
,则双曲线
的离心率为___________ .
![](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/96c4088276acdbede4781b2ebc466366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff00fc29b9b9374935cf7bd256fb6234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2022-04-29更新
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4卷引用:广东省清远市博爱学校2022-2023学年高二上学期第二次教学质量检测数学试题
广东省清远市博爱学校2022-2023学年高二上学期第二次教学质量检测数学试题江西省南昌市2022届高三第二次模拟测试数学(文)试题新疆乌鲁木齐市第101中学2022-2023学年高二上学期期中数学试题(已下线)3.3 抛物线(练习)-高二数学同步精品课堂(苏教版2019选择性必修第一册)
名校
解题方法
6 . 过抛物线
的焦点作直线交抛物线于
两点,如果
,那么
=__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4daf40bad1cc89311930cce356672354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4ee9950e39d2f5aab84316555d1732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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2022-04-19更新
|
360次组卷
|
4卷引用:广东省佛山市南海区南海中学2021-2022学年高二下学期期中数学试题
广东省佛山市南海区南海中学2021-2022学年高二下学期期中数学试题云南省宣威市第三中学2021-2022学年高二4月考试数学试题(已下线)高二上学期期中【夯实基础60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)江西省宜春市丰城中学2024届高三上学期12月段考数学试题
7 . 设抛物线
:
的焦点为
,点
在
上,
,若以
为直径的圆过点
,则
的焦点到其准线的距离为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532bcbe8307e6b2129bdcdbd553ee5f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2022-04-03更新
|
573次组卷
|
3卷引用:广东省普宁市普师高级中学2023届高三二模数学试题
8 . 已知抛物线方程
,
为焦点,
为抛物线准线上一点,
为线段
与抛物线的交点,定义:
.已知点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e711fdfad430a02aff0705d4a2e6b17a.png)
___________ ;设点
,若
恒成立,则
的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fd86488450b45987465e83094bf183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ad63077bd5c3e70db36b608beb0b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e711fdfad430a02aff0705d4a2e6b17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48490c1cb1414f24d493b55755d6d5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600c261b030650beda92627562e7fd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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|
1144次组卷
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3卷引用:广东省惠州市2023届高三上学期第一次调研数学试题
9 . 已知椭圆
的焦点分别为
,
,且
是抛物线
焦点,若P是
与
的交点,且
,则
的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c00e8a3af8a96c98ca1b88fd810669.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c9c87eba774f6bc072663d32d11fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/837822d134751db0cb500690ec544e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab35a31b756427c3458d5ab2024e860c.png)
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2022-03-24更新
|
1918次组卷
|
5卷引用:广东省茂名市2022届高三下学期调研(一)数学试题
10 . 若抛物线
:
上的一点
到它的焦点的距离为3,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34df226b1eb82515842ab0799f71a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
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