名校
解题方法
1 . 如图,过抛物线
焦点F作直线
交抛物线于A,B两点,点M是线段AB的中点,过M作
轴的垂线交抛物线于P点,则
的值为__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72af512abe7f4437e88919f5978c3f.png)
![](https://img.xkw.com/dksih/QBM/2020/8/10/2524927743574016/2527670660595712/STEM/dbd8ef57-5359-4a43-82b4-66ef18a60803.png)
您最近一年使用:0次
2020-08-14更新
|
256次组卷
|
2卷引用:浙江省湖州中学2020届高三下学期高考模拟测试(一)数学试题
名校
解题方法
2 . 如图,过抛物线
焦点
的直线交抛物线于
,
两点,记以
,
为直径端点的圆为圆
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/9769ebff-dc49-48c3-816e-e895c4d2d521.png?resizew=207)
(1)证明:圆
与抛物线的准线相切;
(2)设
,点
在焦点的右侧,圆
与
轴交于
,
两点,记
和
的面积为
,
求
的最大值(其中,点
为圆
与抛物线准线的切点)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/9769ebff-dc49-48c3-816e-e895c4d2d521.png?resizew=207)
(1)证明:圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922f44810de957109599d2236cb84892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/ccd91572cca65c8c052090976e9d1a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
解题方法
3 . 已知抛物线
,其焦点为
,准线为
,过焦点
的直线交抛物线
于点
、
(其中
在
轴上方),
,
两点在抛物线的准线上的投影分别为
,
,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38544c35c45a692f3f1c8dbcdb9db71e.png)
____________ .
![](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/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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bc3e05981a9b9ac5441dd0a03a37d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c504b7cab7c2e3be16b45e47b27f0f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38544c35c45a692f3f1c8dbcdb9db71e.png)
您最近一年使用:0次
2020-05-09更新
|
1652次组卷
|
7卷引用:浙江省温州市瑞安中学2020-2021学年高二上学期期中数学试题
浙江省温州市瑞安中学2020-2021学年高二上学期期中数学试题2020届安徽省皖南八校高三第三次联考数学(文)试题江苏省南通市海安高级中学2021-2022学年高三上学期期中模拟数学试题(已下线)专题05 《圆锥曲线与方程》中的压轴题(1)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) 江西省抚州市临川第一中学2021-2022学年高二下学期第一次月考数学(理)试题河南省濮阳市第一高级中学2021-2022学年高二下学期第一次质量检测数学(理)试题宁夏银川市永宁县第二中学高级中学2021届高考数字诊断性文科试题
名校
解题方法
4 . 抛物线
(
)的焦点为F,直线l过点F且与抛物线交于点M,N(点N在轴上方),点E为轴上F右侧的一点,若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d414c07b1f1a0dc6c1af9525920b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926e78d4a939ba94c572bc9dc6ffd718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
A.1 | B.2 | C.3 | D.9 |
您最近一年使用:0次
2020-04-13更新
|
360次组卷
|
4卷引用:2020届浙江省杭州市学军中学高三下学期3月月考数学试题
2020届浙江省杭州市学军中学高三下学期3月月考数学试题2020年浙江省新高考考前原创冲刺卷(八)(已下线)考点29 抛物线及其性质-2021年高考数学三年真题与两年模拟考点分类解读(新高考地区专用)(已下线)专题6.3 双曲线与抛物线的性质与应用-备战2021年高考数学精选考点专项突破题集(新高考地区)
5 . 以下关于圆锥曲线的命题中:
①双曲线
与椭圆
有相同焦点;
②以抛物线的焦点弦(过焦点的直线截抛物线所得的线段)为直径的圆与抛物线的准线是相切的;
③设
、
为两个定点,
为常数,若
,则动点
的轨迹为双曲线;
④过抛物线
的焦点作直线与抛物线相交于
、
,则使它们的横坐标之和等于5的直线有且只有两条;
以上命题正确的个数为( )
①双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a0bd4bd9985f1e367c100b453ed03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608d1a8669aa2426e12751dec3e96da6.png)
②以抛物线的焦点弦(过焦点的直线截抛物线所得的线段)为直径的圆与抛物线的准线是相切的;
③设
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de09de34461d205f4dd1ba9feddd311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
④过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
以上命题正确的个数为( )
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2020-02-27更新
|
385次组卷
|
3卷引用:浙江省宁波市九校2019-2020学年高二上学期期末联考数学试题
浙江省宁波市九校2019-2020学年高二上学期期末联考数学试题(已下线)第41练 解析几何的综合问题-2021年高考数学(文)一轮复习小题必刷云南省玉溪市新平县第一中学2021-2022学年高二上学期期末素质测试数学试题
6 . 过抛物线
焦点
的直线与该抛物线交于
两点, 再过点
作线段
的垂线,交抛物线的准线于点
,若
,
为坐标原点,则
=___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e9a4a58a149c957a2b2d12a7260434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc66278e55cefbb7749c0d37a7fd6f1e.png)
您最近一年使用:0次
7 . 已知F为抛物线
的焦点,过点F的直线交抛物线于A,B两点,其中A在x轴上方,O是坐标原点,若
,
,则以AB为直径的圆的标准方程为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2171a7e806dc496b06bfe0a3a043e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7d86dfc77fa2e07f08a732378a09a2.png)
您最近一年使用:0次
名校
8 . 如图,过抛物线
的焦点F的直线交抛物线于点A,B,交其准线l于点C,若F是AC的中点,且
,则线段AB的长为( )
![](https://img.xkw.com/dksih/QBM/2020/8/7/2522772535590912/2524772919271424/STEM/5b24ba51df80412c9d36ad29470fc1b6.png?resizew=142)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56bbafa889700c6764ebc7fc1a42cd91.png)
![](https://img.xkw.com/dksih/QBM/2020/8/7/2522772535590912/2524772919271424/STEM/5b24ba51df80412c9d36ad29470fc1b6.png?resizew=142)
A.5 | B.6 | C.![]() | D.![]() |
您最近一年使用:0次
2020-08-10更新
|
2542次组卷
|
19卷引用:浙江省亳州市2017-2018学年高二第一学期期末质量检测理科数学试题
浙江省亳州市2017-2018学年高二第一学期期末质量检测理科数学试题湖南省益阳市、湘潭市2018届高三9月调研考试数学(理)试题【全国百强校】内蒙古赤峰二中2019届高三上学期第二次月考数学(理)试题内蒙古巴彦淖尔一中2018-2019学年高二上学期期中考试数学(文)试题内蒙古巴彦淖尔一中2018-2019学年高二上学期期中考试数学(理)试卷【全国百强校】甘肃省天水市第一中学2018-2019学年高二上学期第二学段考试数学(文)试题河北省石家庄市第二中学2019-2020学年高二上学期期中数学试题山东省滨州市博兴县2018-2019学年高二上学期期中数学试题2019届百师联盟全国高三模拟考(二)全国II卷文科数学试卷(已下线)测试卷23 抛物线(B)-2021届高考数学一轮复习(文理通用)单元过关测试卷陕西省西安市长安区第一中学2020-2021学年高二上学期期中数学(理)试题陕西省咸阳市实验中学2020-2021学年高二上学期第四次月考数学(理)试题黑龙江省实验中学2021-2022学年高二上学期期中数学试题陕西省咸阳市武功县普集高中2021-2022学年高二上学期第三次月考理科数学试题(已下线)专题9 圆锥曲线第二定义的应用 微点3 圆锥曲线第二定义的应用综合训练(已下线)11.3 抛物线(已下线)专题12 圆锥曲线压轴小题常见题型全归纳(精讲精练)-1宁夏吴忠市2023届高三下学期一轮联考数学(文)试题(已下线)第七节 抛物线 第一课时 抛物线的定义、方程与性质 讲
名校
解题方法
9 . 已知
是抛物线
的焦点,
是抛物线
上一点过
三点的圆的圆心为
,点
到抛物线
的准线的距离为
.
![](https://img.xkw.com/dksih/QBM/2020/3/31/2431484446023680/2431548928442368/STEM/fcf72c71-45e8-4d9b-81e1-34fcd80213aa.png?resizew=290)
(1)求抛物线
的方程;
(2)若点
的横坐标为4,过
的直线
与抛物线
有两个不同的交点
,直线
与圆
交于点
,且点
的横坐标大于4,求当
取得最小值时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.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/76e4a04771a93c113c8617588daba23d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://img.xkw.com/dksih/QBM/2020/3/31/2431484446023680/2431548928442368/STEM/fcf72c71-45e8-4d9b-81e1-34fcd80213aa.png?resizew=290)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](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/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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06935e279652219a5f4f37cace92483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
10 . 已知抛物线
,过抛物线C的焦点F作互相垂直的两条直线AB,CD,与抛物线C分别相交于A,B和C,D,点A,C在x轴上方.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/a67b15e1-bf70-42b3-9b15-b8b2415af2ae.png?resizew=159)
(1)若直线AB的倾斜角为
,求
的值;
(2)设
与
的面积之和为S,求S的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/a67b15e1-bf70-42b3-9b15-b8b2415af2ae.png?resizew=159)
(1)若直线AB的倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260200d547998bcac50a4a491382e7f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36691f0269294ecae8f00b7bce97756c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25d95565e1e7f522624ed32e5a61199.png)
您最近一年使用:0次
2020-03-22更新
|
327次组卷
|
2卷引用:浙江省舟山市2018-2019学年高二上学期期末数学试题