過點(diǎn)(2,-2)且與雙曲線
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_ST/0.png)
-y
2=1有公共漸近線的雙曲線方程是( )
A.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_ST/1.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_ST/2.png)
=1
B.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_ST/3.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_ST/4.png)
=1
C.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_ST/5.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_ST/6.png)
=1
D.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_ST/7.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_ST/8.png)
=1
【答案】
分析:設(shè)所求雙曲線方程為
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_DA/0.png)
-y
2=λ,把(2,-2)代入方程
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_DA/1.png)
-y
2=λ,求出λ,可得到所求的雙曲線方程.
解答:解:設(shè)所求雙曲線方程為
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_DA/2.png)
-y
2=λ,
把(2,-2)代入方程
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_DA/3.png)
-y
2=λ,
解得λ=-2.由此可求得所求雙曲線的方程為
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214638843102243/SYS201310232146388431022001_DA/4.png)
.
故選A.
點(diǎn)評(píng):本題考查雙曲線的漸近線方程,解題時(shí)要注意公式的靈活運(yùn)用.
練習(xí)冊(cè)系列答案
相關(guān)習(xí)題
科目:高中數(shù)學(xué)
來源:
題型:
過點(diǎn)(2,-2)且與雙曲線
-y
2=1有公共漸近線的雙曲線方程是( )
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:
題型:
過點(diǎn)(2,-2)且與
-y2=1有公共漸近線方程的雙曲線方程為
.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:
題型:
過點(diǎn)(-2,2)且與兩坐標(biāo)軸圍成的三角形面積為1的直線的斜率為( )
| |
| |
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:2012-2013學(xué)年福建省廈門二中高二(上)數(shù)學(xué)周末練習(xí)13(文科)(解析版)
題型:選擇題
過點(diǎn)(2,-2)且與雙曲線
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103104139123321818/SYS201311031041391233218003_ST/0.png)
-y
2=1有公共漸近線的雙曲線方程是( )
A.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103104139123321818/SYS201311031041391233218003_ST/1.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103104139123321818/SYS201311031041391233218003_ST/2.png)
=1
B.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103104139123321818/SYS201311031041391233218003_ST/3.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103104139123321818/SYS201311031041391233218003_ST/4.png)
=1
C.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103104139123321818/SYS201311031041391233218003_ST/5.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103104139123321818/SYS201311031041391233218003_ST/6.png)
=1
D.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103104139123321818/SYS201311031041391233218003_ST/7.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131103104139123321818/SYS201311031041391233218003_ST/8.png)
=1
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:2010-2011學(xué)年河北省張家口市高二(上)期末數(shù)學(xué)試卷(理科)(解析版)
題型:選擇題
過點(diǎn)(2,-2)且與雙曲線
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101225557240776411/SYS201311012255572407764003_ST/0.png)
-y
2=1有公共漸近線的雙曲線方程是( )
A.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101225557240776411/SYS201311012255572407764003_ST/1.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101225557240776411/SYS201311012255572407764003_ST/2.png)
=1
B.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101225557240776411/SYS201311012255572407764003_ST/3.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101225557240776411/SYS201311012255572407764003_ST/4.png)
=1
C.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101225557240776411/SYS201311012255572407764003_ST/5.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101225557240776411/SYS201311012255572407764003_ST/6.png)
=1
D.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101225557240776411/SYS201311012255572407764003_ST/7.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101225557240776411/SYS201311012255572407764003_ST/8.png)
=1
查看答案和解析>>