Keen on/at? phrasal verb usage

Please help me fill and explain the following sentences.

1. You don't seem keen ____ playing tennis.
My answer is keen on but I am not sure about the explanation.

2. She is keen ___ watch the movie.
She is keen _____ watching the movie.

For the first one, i think it is 'keen to' watch the movie. And for the second, I think it is 'keen on'. Can you let me know why the prepositions can change?

Thank you!

Question

Keen on/at? phrasal verb usage

Please help me fill and explain the following sentences.

1. You don't seem keen ____ playing tennis.
My answer is keen on but I am not sure about the explanation.

2. She is keen ___ watch the movie.
She is keen _____ watching the movie.

For the first one, i think it is 'keen to' watch the movie. And for the second, I think it is 'keen on'. Can you let me know why the prepositions  can change?

Thank you!

Answer

I believe your answer is correct.  'Keen' is used in British English, and since I'm American I'm not an expert on this matter.  I would use 'to' with the infinitive and 'on' with the gerund.