名校
解题方法
1 . 已知曲线
上一动点
到两定点
,
的距离之和为
,过点
的直线
与曲线
相交于点
,
.
(1)求曲线
的方程;
(2)动弦
满足:
,求点
的轨迹方程;
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f7a7cf83fb9706134edb619d8aa90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cc3f576dcf32e3ec2de59ea8059a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14dd75003428d5b4071aabbaa4d11cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)动弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55899a55390743a4dd830402641d2122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f979df095c33a0d8edce5c1fab7cad04.png)
您最近一年使用:0次
2022-09-06更新
|
380次组卷
|
2卷引用:上海市行知中学2022届高三上学期开学考试数学试题
名校
解题方法
2 . 一般地,如果函数
的定义域为
,值域也是
,则称函数
为“保域函数”,下列函数中是“保域函数”的有_________ .(填上所有正确答案的序号)
①
,
; ②
,
;
③
,
; ④
,
;
⑤
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19024088b481805fd372b7b2ffdd8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928dc7b88802aa89c8f0071c66b3c628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3afa36d64d3fe306d08480a7845f28ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c6190c7d27f739d39812e20e83af684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7973e7275ff254569d0abfb03cc5c875.png)
⑤
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ccf41f4af0298c2f40e0d38a8ff682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
您最近一年使用:0次
2021高二·全国·专题练习
解题方法
3 . 渐近线的斜率能否用来判断某些直线与双曲线的位置关系及交点位置.
您最近一年使用:0次
2021高二·全国·专题练习
名校
4 . 有一座抛物线型拱桥,其水面宽AB为18米,拱顶O离水面AB的距离OM为8米,货船在水面上的部分的横断面是矩形CDEF,如图建立平面直角坐标系.
![](https://img.xkw.com/dksih/QBM/2022/1/5/2887837411631104/2953193576333312/STEM/e8dde07ddd404d079b379d854f080b32.png?resizew=230)
(1)求此抛物线的解析式;
(2)如果限定矩形的长CD为9米,那么矩形的高DE不能超过多少米,才能使船通过拱桥.
(3)若设EF=a,请将矩形CDEF的面积S用含a的代数式表示,并指出a的取值范围.
![](https://img.xkw.com/dksih/QBM/2022/1/5/2887837411631104/2953193576333312/STEM/e8dde07ddd404d079b379d854f080b32.png?resizew=230)
(1)求此抛物线的解析式;
(2)如果限定矩形的长CD为9米,那么矩形的高DE不能超过多少米,才能使船通过拱桥.
(3)若设EF=a,请将矩形CDEF的面积S用含a的代数式表示,并指出a的取值范围.
您最近一年使用:0次
2021高一上·江苏·专题练习
5 . 下列命题中:
若
,则关于x的方程
有实根;
若
,则
;
;
是一元二次方程
有一正根和一负根的充要条件.
其中是真命题的有_________
填上所有真命题的序号
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0c232e07b0adf5c19e888881fe7cdaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da28fb5de5ea0265582e6e78640708da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9e131cdd242d56b6dba05ab3363ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef193f44b2af4159e5f32eb0e2524762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d0b9d0da4a7d99a8e9ed5d779e3643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fa32c1e926f40a0722d106563777ef.png)
其中是真命题的有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
您最近一年使用:0次
2022高三·全国·专题练习
名校
解题方法
6 . 若两个椭圆的离心率相等,则称它们为“相似椭圆”.如图,在直角坐标系xOy中,已知椭圆C1:
,A1,A2分别为椭圆C1的左,右顶点.椭圆C2以线段A1A2为短轴且与椭圆C1为“相似椭圆”.
![](https://img.xkw.com/dksih/QBM/2021/9/12/2806673426440192/2807831992770560/STEM/8273a057-f3fe-40fd-b75b-539aa9536268.png?resizew=203)
(1)求椭圆C2的方程;
(2)设P为椭圆C2上异于A1,A2的任意一点,过P作PQ⊥x轴,垂足为Q,线段PQ交椭圆C1于点H.求证:H为△PA1A2的垂心.(垂心为三角形三条高的交点)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c03c6b8d7418edf20f474389971352.png)
![](https://img.xkw.com/dksih/QBM/2021/9/12/2806673426440192/2807831992770560/STEM/8273a057-f3fe-40fd-b75b-539aa9536268.png?resizew=203)
(1)求椭圆C2的方程;
(2)设P为椭圆C2上异于A1,A2的任意一点,过P作PQ⊥x轴,垂足为Q,线段PQ交椭圆C1于点H.求证:H为△PA1A2的垂心.(垂心为三角形三条高的交点)
您最近一年使用:0次
2021-09-14更新
|
0次组卷
|
4卷引用:3.1.2椭圆的简单几何性质(备作业)-【上好课】2021-2022学年高二数学同步备课系列(人教A版2019选择性必修第一册)
(已下线)3.1.2椭圆的简单几何性质(备作业)-【上好课】2021-2022学年高二数学同步备课系列(人教A版2019选择性必修第一册)(已下线)专题41椭圆-2022年(新高考)数学高频考点+重点题型广东省江门市新会陈经纶中学2022届高三上学期9月月考数学试题沪教版(2020) 选修第一册 新课改一课一练 期末测试C
2021高二·江苏·专题练习
解题方法
7 . 某路旁有一个小区域,经过整理可利用三点合理建一个
形状的指示灯台,如图,设计师通过测量可知这三处恰为某曲线上三点
,
,
,
,则指示灯台最大可能建成的面积为
参考数据:
,
( )
![](https://img.xkw.com/dksih/QBM/2022/1/2/2885860476862464/2887142578511872/STEM/70c51f210cbe4bd3949ef34b6bb9511a.png?resizew=319)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704b6bdee6dc5ef6ad56aa329cdc6d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4857c170b32122e630720c7ceb031d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc94d53a71c46df7809c6f5d8c9e4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d438267fddcd02afff8e73c6c3fec8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4191454bebd60d62113ffd5560f121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1bb9a72c862ccc8e78350a43a06e34e.png)
![](https://img.xkw.com/dksih/QBM/2022/1/2/2885860476862464/2887142578511872/STEM/70c51f210cbe4bd3949ef34b6bb9511a.png?resizew=319)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021高二·江苏·专题练习
名校
8 . 已知函数
在
内连续且可导,其导函数为
,且满足
,
恒成立,则下列命题正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f68c6ed09e483db6edf0b4caf5e252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e808873b814cf720131eeed83e88bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c47f804276a27d23baba42e970cabde.png)
A.函数![]() ![]() |
B.![]() ![]() |
C.曲线![]() ![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2021高二·江苏·专题练习
解题方法
9 . 已知圆
.
(1)过直线
上点P作圆
的两条切线,若两条切线的夹角是
,求点P的坐标;
注:两条直线相交所形成的小于等于
的正角称为这两条直线的夹角![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(2)点
,
,动点P始终满足
试判断动点P的轨迹
与圆
的位置关系;
(3)过曲线
上的点
作直线
和
,与曲线
另分别相交于点M,N,若
与
的斜率互为相反数,问直线
的斜率是否为定值,若是求出该定值,若不是请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70feca8eac775ebee7b6d9760e2be6f6.png)
(1)过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bab7b913a04839bb9d4f1d5c8ce64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774480361088aa3198c7bc3148fa23fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6711f23c2900c7b00a833bf21edb23d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b360e2cfc9077a2deafa9d3d5f7afb30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(3)过曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519e7d52725f9f6d1b6bb7966052921c.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/b1241216f3c1cb5e73043dd1037f556d.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/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2021高二·江苏·专题练习
名校
10 . 如图,矩形OABC中,
,以O为圆心,OC为半径作圆与OA相交于点D,在BC上取一点E,OA上取一点F,使得EF与
相切与点G,则四边形OFEC的面积取得最小值时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed2b6aae7585e2a76557369da4e43ee.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497e34cb645ed931bea31c5d4c558c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed2b6aae7585e2a76557369da4e43ee.png)
![](https://img.xkw.com/dksih/QBM/2022/1/2/2885860476862464/2887142579552256/STEM/3df444b045e84d9882b7b2770c05f142.png?resizew=260)
您最近一年使用:0次
2022-01-04更新
|
720次组卷
|
4卷引用:专题14 《导数及其应用》中的周长和面积问题-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)
(已下线)专题14 《导数及其应用》中的周长和面积问题-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) 湖南省长沙市长郡中学2022届高三下学期押题卷1数学试题广东省揭阳市普宁国贤学校2023届高三下学期3月连考3数学试题(已下线)2024届数学新高考Ⅰ卷精准模拟(五)