The will be used before Tea because – Here, we are talking about a particular tea, followed by a Relative Pronoun (which). The sentence can also be written as –

The tea I am drinking is hot (tea-definite) Look at the examples given below : The flowers in her garden are beautiful. (Definite – the ones in her garden)

The flowers (that) are in her  

↓

Rel.pro.

garden are beautiful.

The dog in the backyard is very cute. (Definite-the one in the backyard)

The dog (which) is in the backyard is very cute.

↓

Rel.pro.

Hence, the tea is the right usage.

the will be used before poor because – the (Def. Art.) is used with Adjectives to refer to a thing or a group of people described by the Adj. Look at the examples given below :

The poor always suffer

↓     ↓

Def. Art. Adj. (refers to a group of people who are poor) He is collecting money for the blind.

                                                                                                                                                     ↓

                                                                                                                                                Def. Art.

blind refers to a group of people who are blind.

hearing will replace hear because – Phrasal Verbs are always followed by Gerunds. Here, look forward to is a Phr. V. Look at the examples given below :

He was accused of smuggling contraband goods.

                  ↓                   ↓

                 Phr.V            Gerund

He insisted on proof-reading the article again.

                  ↓                   ↓

                 Phr.V            Gerund

at will replace by because – Shocked always agrees with at (Prep.) at is used with Adjectives for showing the cause of something. Look at the examples given below : They were impatient at the delay. She was delighted at the result. Here, shocked is the Adj. and it is indicating the Cause (reason) of the actress’s shock. Hence, at the news of her dog’s death is the right usage