名校
1 . 已知直线
,
与抛物线
相交于A,B两点,F为抛物线的焦点,若
,则k=______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1609abfd5ad3143c3f77378df927d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a083af79190de95296ab449077b4e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9e01533bd74173d7e0a352a1a64464.png)
您最近一年使用:0次
2020-11-14更新
|
328次组卷
|
5卷引用:广西陆川县中学2016-2017学年高二下学期知识竞赛数学(理)试题
2 . 已知椭圆C:
(a>b>0)的左、右焦点分别为F1,F2,离心率为
,且经过点(1,
).
(1)求椭圆C的方程;
(2)动直线l:y=x+m与椭圆C相切,点M,N是直线l上的两点,且F1M⊥l,F2N⊥l,求四边形F1MNF2的面积;
(3)过椭圆C内一点T(t,0)作两条直线分别交椭圆C于点A,C,和B,D,设直线AC与BD的斜率分别是k1,k2,若|AT|·|TC|=|BT|·|TD|,试问k1+k2是否为定值,若是,求出定值,若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(1)求椭圆C的方程;
(2)动直线l:y=x+m与椭圆C相切,点M,N是直线l上的两点,且F1M⊥l,F2N⊥l,求四边形F1MNF2的面积;
(3)过椭圆C内一点T(t,0)作两条直线分别交椭圆C于点A,C,和B,D,设直线AC与BD的斜率分别是k1,k2,若|AT|·|TC|=|BT|·|TD|,试问k1+k2是否为定值,若是,求出定值,若不是,说明理由.
您最近一年使用:0次
2022-07-07更新
|
933次组卷
|
6卷引用:广西陆川县中学2016-2017学年高二下学期知识竞赛数学(理)试题
3 . 已知抛物线
内一定点
,过点
分别作斜率为
,
的两条直线
、
,交抛物线于
、
和
、
四点,设
、
分别为线段
和
的中点.
(1)当
且
时,求
的面积的最小值;
(2)若
(
为常数,且
),证明:直线
过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc5dd4d07e2098d8d1b731f2622867f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/8455657dde27aabe6adb7b188e031c11.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd09fb9482124fd35f19b86894648f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257beb71337358f5ccc57219d9153666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e860e7d762c206d296cffbdd2786e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78fbecca12ee62538020483fd55a2109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
名校
解题方法
4 . 已知中心在原点的椭圆
的两焦点分别为双曲线
的顶点,直线
与椭圆
交于
、
两点,且
,点
是椭圆
上异于
、
的任意一点,直线
外的点
满足
,
.
(1)求点
的轨迹方程;
(2)试确定点
的坐标,使得
的面积最大,并求出最大面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea74737939c0f94c91229a7098f36ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d373ef598634c09fd59744f8411d4037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/b0d22b413e83596b011dd23e25d4090f.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad492faa37d468027765399b64574439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0e65c1d8e47c4698ced909db38ec2c.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)试确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
您最近一年使用:0次
2017-04-01更新
|
805次组卷
|
2卷引用:2017届广西陆川县中学高三下学期知识竞赛理数试卷