curious to explore是什么使用方法

请教老师 After the class, we all quickly ran out the door,curious to explore this new world we had just entered.老师麻烦问一下这里curious toexplore是什么使用方法呀, curious这个形容词加上的不定式是只能放在句子的末尾吗,还有为何不是curious exploring？

After class, we all quickly ran out the door, curious to explore this new world we had just entered.

整个形容词短语作前文是什么原因状语。

大家说 be curious to do sth.，不说 be curious doing sth. ，这就是不可以用 curious exploring 是什么原因。