已知中心在原點(diǎn),焦點(diǎn)在坐標(biāo)軸上的雙曲線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043326313.png)
經(jīng)過
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043341556.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043419510.png)
兩點(diǎn)
(1)求雙曲線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043326313.png)
的方程;
(2)設(shè)直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043466612.png)
交雙曲線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043326313.png)
于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043497399.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043513357.png)
兩點(diǎn),且線段
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043529513.png)
被圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043544318.png)
:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043560988.png)
三等分,求實(shí)數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043575339.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043591277.png)
的值
試題分析:(1)求雙曲線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043326313.png)
的方程,可設(shè)雙曲線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043326313.png)
的方程是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043747689.png)
,利用待定系數(shù)法求出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043763437.png)
的值即可,由雙曲線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043326313.png)
經(jīng)過
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043341556.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043419510.png)
兩點(diǎn),將
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043341556.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043419510.png)
代入上面方程得,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043887999.png)
,解方程組,求出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043763437.png)
的值,即可求出雙曲線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043326313.png)
的方程;(2)求實(shí)數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043575339.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043591277.png)
的值,直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043466612.png)
交雙曲線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043326313.png)
于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043497399.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043513357.png)
兩點(diǎn),且線段
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043529513.png)
被圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043544318.png)
:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043560988.png)
三等分,可知圓心與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043529513.png)
的中點(diǎn)垂直,設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043529513.png)
的中點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044121638.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044137481.png)
,而圓心
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044168559.png)
,因此只需找出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043529513.png)
的中點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044121638.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043575339.png)
的關(guān)系,可將
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043466612.png)
代人
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043607588.png)
,得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044262893.png)
,設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044309996.png)
,利用根與系數(shù)關(guān)系及中點(diǎn)坐標(biāo)公式得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044340647.png)
,這樣可求得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043575339.png)
的值,由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043575339.png)
的值可求出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044543543.png)
的長,從而得圓的弦長,利用勾股定理可求得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043591277.png)
的值
試題解析:(1)設(shè)雙曲線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043326313.png)
的方程是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043747689.png)
,依題意有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043887999.png)
2分
解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044652571.png)
3分 所以所求雙曲線的方程是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043607588.png)
4分
(2)將
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043466612.png)
代人
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043607588.png)
,得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044262893.png)
(*)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240340447611163.png)
6分
設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044309996.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043529513.png)
的中點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044121638.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044823621.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044839654.png)
7分
則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044855801.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044870674.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044901662.png)
8分
又圓心
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044168559.png)
,依題意
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044137481.png)
,故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044948650.png)
,即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043622450.png)
9分
將
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043622450.png)
代人(*)得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044995611.png)
,解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034045011540.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240340450261171.png)
10分
故直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034045042280.png)
截圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043544318.png)
所得弦長為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034045089879.png)
,又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034044168559.png)
到直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034045042280.png)
的距離
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034045229508.png)
11分
所以圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043544318.png)
的半徑
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034045260976.png)
所以圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043544318.png)
的方程是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034045291759.png)
12分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034045307468.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034043638489.png)
13分
練習(xí)冊系列答案
相關(guān)習(xí)題
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240401069761239.png)
的離心率為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040106992413.png)
,且經(jīng)過點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040107008657.png)
過坐標(biāo)原點(diǎn)的直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040107008314.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040107023339.png)
均不在坐標(biāo)軸上,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040107008314.png)
與橢圓M交于A、C兩點(diǎn),直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040107023339.png)
與橢圓M交于B、D兩點(diǎn)
(1)求橢圓M的方程;
(2)若平行四邊形ABCD為菱形,求菱形ABCD的面積的最小值
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)橢圓的方程為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240341114371132.png)
,斜率為1的直線不經(jīng)過原點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111453293.png)
,而且與橢圓相交于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111468409.png)
兩點(diǎn),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111484383.png)
為線段
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111484374.png)
的中點(diǎn).
(1)問:直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111500441.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111484374.png)
能否垂直?若能,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111531385.png)
之間滿足的關(guān)系式;若不能,說明理由;
(2)已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111484383.png)
為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111546417.png)
的中點(diǎn),且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111562342.png)
點(diǎn)在橢圓上.若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111578701.png)
,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034111531385.png)
之間滿足的關(guān)系式.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)一個焦點(diǎn)為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054386228.png)
,且離心率
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054402516.png)
的橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240340544331165.png)
上下兩頂點(diǎn)分別為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054495423.png)
,直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054511575.png)
交橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054527306.png)
于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054542412.png)
兩點(diǎn),直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054558360.png)
與直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054573481.png)
交于點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054589381.png)
.
(1)求橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054527306.png)
的方程;
(2)求證:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034054620604.png)
三點(diǎn)共線.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知動直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950723280.png)
與橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950723319.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950738710.png)
交于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950754289.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950769573.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950801328.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950816587.png)
兩不同點(diǎn),且△
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950832452.png)
的面積
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950847522.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950863471.png)
,其中
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950879292.png)
為坐標(biāo)原點(diǎn).
(1)證明
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950894484.png)
和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950910514.png)
均為定值;
(2)設(shè)線段
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950925413.png)
的中點(diǎn)為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950925400.png)
,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950957659.png)
的最大值;
(3)橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950972313.png)
上是否存在點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033950988533.png)
,使得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240339510191127.png)
?若存在,判斷△
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033951035489.png)
的形狀;若不存在,請說明理由.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240339156691091.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915669474.png)
,若橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240339156851165.png)
的右頂點(diǎn)為圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915701399.png)
的圓心,離心率為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915716413.png)
.
(1)求橢圓C的方程;
(2)若存在直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915732536.png)
,使得直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915747272.png)
與橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915747306.png)
分別交于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915779423.png)
兩點(diǎn),與圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915701399.png)
分別交于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915810430.png)
兩點(diǎn),點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915810312.png)
在線段
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915825396.png)
上,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915872608.png)
,求圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915701399.png)
的半徑
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033915888260.png)
的取值范圍.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知拋物線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736578313.png)
的頂在坐標(biāo)原點(diǎn),焦點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736609724.png)
到直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736609482.png)
的距離是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736625455.png)
(1)求拋物線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736578313.png)
的方程;
(2)若直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736656774.png)
與拋物線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736578313.png)
交于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736687423.png)
兩點(diǎn),設(shè)線段
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736703396.png)
的中垂線與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736703310.png)
軸交于點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736734533.png)
,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033736734299.png)
的取值范圍.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843275765.png)
的左、右焦點(diǎn)分別為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843291333.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843307352.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843322291.png)
為原點(diǎn).
(1)如圖1,點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843322399.png)
為橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843338306.png)
上的一點(diǎn),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843353351.png)
是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843369498.png)
的中點(diǎn),且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843385725.png)
,求點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843322399.png)
到
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843525310.png)
軸的距離;
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240328435412126.png)
(2)如圖2,直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843556658.png)
與橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843338306.png)
相交于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843587289.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843603333.png)
兩點(diǎn),若在橢圓
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843338306.png)
上存在點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843634303.png)
,使四邊形
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843650491.png)
為平行四邊形,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824032843665337.png)
的取值范圍.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240328436812317.png)
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知橢圓
C1:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034407000691.png)
=1,橢圓
C2以
C1的短軸為長軸,且與
C1有相同的離心率.
(1)求橢圓
C2的方程;
(2)設(shè)直線
l與橢圓
C2相交于不同的兩點(diǎn)
A、
B,已知
A點(diǎn)的坐標(biāo)為(-2,0),點(diǎn)
Q(0,
y0)在線段
AB的垂直平分線上,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034407015561.png)
=4,求直線
l的方程.
查看答案和解析>>