meaning in context - Contextual difference between "That is why" vs "Which is why"?

Please consider the below sentences.

I have flunked the exam, that is why I am attending coaching classes.
I have flunked the exam, which is why I am attending coaching classes.

Is there any change in the meaning of sentence if I replace That is why with Which is why? For me both are suitable for the above context and unable to differentiate change in the meaning.