Glad to hear it / this / that - are all of these correct?

You will find on this page quite a few instances of "I am glad to hear this.", and the form you consider is nothing else than an ellipted version of that; this ellipsis of the subject and verb is usual (albeit colloquial) for this construction (I am < ADJ > to < base form of verb > < completing elements (their total length must be relatively short)>) and for certain adjectives, but not all. It is also used for the third person and for certain adjectives. The adjective "glad" is one of the "permitted" adjectives; therefore, there is no reason not to use this construction for "glad" with any object (any object that makes sense), and in particular with "this".

Examples

• Glad to hear it/this/that/you'll come/it's finished/you say that….
• Happy to see (that) you succeeded (in solving that equation/in convincing your friend/in bringing your brother back home/…)
• Not really happy to buy that but there is no choice.
• Sorry to have to tell you again.
• (Not) Sure to make it to the top.
• Bound to happen.

Adjectives for which it does not sound natural and should be avoided (there are many more than those provided in those examples)

• I am reluctant to do this. / Reluctant to do this.
• I am conscious that is not possible. / Conscious that is not possible.