在平面直角坐標(biāo)系xoy中,橢圓E:
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131025125843018401511/SYS201310251258430184015019_ST/0.png)
(a>0,b>0)經(jīng)過點(diǎn)A(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131025125843018401511/SYS201310251258430184015019_ST/1.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131025125843018401511/SYS201310251258430184015019_ST/2.png)
),且點(diǎn)F(0,-1)為其一個(gè)焦點(diǎn).
(Ⅰ)求橢圓E的方程;
(Ⅱ)設(shè)橢圓E與y軸的兩個(gè)交點(diǎn)為A
1,A
2,不在y軸上的動(dòng)點(diǎn)P在直線y=b
2上運(yùn)動(dòng),直線PA
1,PA
2分別與橢圓E交于點(diǎn)M,N,證明:直線MN通過一個(gè)定點(diǎn),且△FMN的周長為定值.