名校
1 . 平面内两定点M(0,-2)和N(0,2),动点P(x,y)满足|PM|·|PN|=
(
≥4),动点P的轨迹为曲线E,给出以下命题:①∃
,使曲线E过坐标原点;②对∀
,曲线E与x轴有三个交点;③曲线E只关于y轴对称,但不关于x轴对称;④若P,M,N三点不共线,则△PMN周长的最小值为
;⑤曲线E上与M,N不共线的任意一点G关于原点对称的点为H,则四边形GMHN的面积不大于
.其中真命题的序号是____________ .(填上所有真命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db20358d559aa21850fcb19e15ac9cb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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