past participles - passive Gerunds to express likes or dislikes

I've read these sentences in my grammar book. And it says "we use I like ... and I don't like+gerund/noun". Example sentences are:

1. I like being obeyed by my students.


2. I don't like being laughed at.


3. I don't like being asked irrelevant questions.

I don't understand it because we can also use the to-infinitive to express like or dislike, for example:

I like to be obeyed by my students.

So, why to use gerunds like above? Could you please tell me about the "being+past participle" form related to gerunds? Is it the passive of the -ing form? If so, how would the sentences look like in active form?

Source: http://www.learnamericanenglishonline.com/Green%20Level/G15%20Gerunds%20Passive.html