名校
1 . 已知抛物线C:的焦点为F,准线为l,过F的直线交抛物线C于A,B两点,
的中垂线分别交l与x轴于D,E两点(D,E在
的两侧).若四边形
为菱形,则
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2 . 如图是一座抛物线型拱桥,当桥洞内水面宽
时,拱顶距离水面
,当水面上升
后,桥洞内水面宽为________
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1e0bd4fe8afb14b572852121cef83d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7854968bbf6576a1fd9926ee0d4d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71a41641aa0d0e45a3c03d3d2c1196b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/59f4b5a0-7bff-4f2b-9684-99e6b50524b6.png?resizew=185)
您最近一年使用:0次
2024高二上·全国·专题练习
解题方法
3 . 已知抛物线
:
的焦点为
,过点
的直线
交
于
,
两点,交
的准线于点
.若
为线段
的中点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b998f232a34711a14a99116248495526.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/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/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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b998f232a34711a14a99116248495526.png)
您最近一年使用:0次
解题方法
4 . 已知抛物线
和
.点
在
上(点
与原点不重合),过点
作
的两条切线,切点分别为
,直线
交
于
两点,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12b5e5ff59f1eea47300d8d7ca9167e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ead5f61654a3b981b10e67b2f2a205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa69fd8445d01c98634c2e885b47d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec33cfe76830902de877bdb208adbb0.png)
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解题方法
5 . 已知抛物线
的焦点为F,过点F作与x轴不垂直的直线l交C于点A,B,过点A作垂直于x轴的直线交C于点D,若点M是
的外心,则
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae0a11e98f07a03035865542297a72f.png)
您最近一年使用:0次
解题方法
6 . 已知抛物线
,过
焦点的直线交
于
,
两点,点
为直线
上的点,且
是等边三角形,则
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
您最近一年使用:0次
解题方法
7 . 已知F为抛物线
(t为参数)的焦点,过F作两条互相垂直的直线
,直线
与C交于A,B两点,直线
与C交于D,E两点,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512d63e6d79877f4407a6a8f68dce3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192aeb9fe486f44a27d837274daf8657.png)
您最近一年使用:0次
2024-02-13更新
|
325次组卷
|
3卷引用:第2章 圆锥曲线 单元综合检测(难点)-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)
(已下线)第2章 圆锥曲线 单元综合检测(难点)-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)陕西省2024届高三教学质量检测(一)文科数学试题陕西省2024届高三教学质量检测(一)理科数学试题
8 . 已知抛物线C:
焦点为F,过点F的直线l与抛物线交于两点
,
.
①若直线l的斜率为1,则弦长
;
②以AB为直径的圆交准线于点D,则
;
③过点A和抛物线顶点的直线交抛物线的准线为点C,则直线
轴且点A的横坐标为1;
④若直线l垂直于对称轴,过抛物线上任一点P作垂直于对称轴的直线,垂足为
,则
、
、
成等比数列.
以上结论中正确的序号为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c663466d641b5fdfef1e529d6c330ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166afeb61d5a80366a8ae29c912cd644.png)
①若直线l的斜率为1,则弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e84da8cdea820c6ae310a1cf9e65d7e.png)
②以AB为直径的圆交准线于点D,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650c6c818df102a83ce5159e3208d01a.png)
③过点A和抛物线顶点的直线交抛物线的准线为点C,则直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2455fb53ada309ffe9717d2613a937f6.png)
④若直线l垂直于对称轴,过抛物线上任一点P作垂直于对称轴的直线,垂足为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2401bc9c26cc3b0b8384c7139bd58fff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d87446c9ef0230285d9b08127fce5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2905ba7cf884768cd68165f6cf02de6b.png)
以上结论中正确的序号为
您最近一年使用:0次
名校
解题方法
9 . 已知抛物线
的焦点为
,直线
均过点
分别交抛物线
于
四点,若直线
斜率乘积的绝对值为8,则当直线
的斜率为___________ 时,
的值最小,最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/0f63a76a5f78eb64e64b5a2c9f1553cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45d4785a48c4e9641450e9ee2822df3.png)
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2024-02-03更新
|
47次组卷
|
2卷引用:广东省高州市某校2023-2024学年高二上学期期末学情数学练习卷
名校
解题方法
10 . 已知O为坐标原点,过抛物线C:
的焦点F的直线与C交于A,B两点,其中A在第一象限,
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0261104a7c308433a0c0508ff20ea29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e67b69730156fac65e5fc32fab57053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188cb9d382147942736d0c5edd806707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
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2024-01-26更新
|
130次组卷
|
2卷引用:江西省上饶市广丰中学2023-2024学年高二上学期期末数学试题