Frame a WH question to get the underlined part as the answer:
I had to go to hospital last week because I had a severe headache.

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Why did you have to go the hospital?

When did you have to go to the hospital?

Where did you have to go to the hospital?

How did you have to go the hospital?

answer is A.

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Detailed Solution

Option a ‘Why did you have got to travel to the hospital?’ portrays the question asking the explanation of visiting the hospital. The statement is that the perfect answer to the question given in option a. So, this feature is correct.
Option b ‘When did you've got to travel to the hospital?’ portrays the question asking the time of visiting the hospital. The statement isn't specifying the time of visiting the hospital. So, this selection is inaccurate.
Option c ‘Where did you have got to travel to the hospital?’ portrays the question asking the place or location of the hospital. The statement isn't specifying the place of the hospital. So, this feature is inaccurate.
Option d ‘How did you have got to travel to the hospital?’ portrays the question of the style of visiting the hospital. The statement isn't specifying the way of visiting the hospital. So, this feature is additionally incorrect.
So, the proper answer is “Option a”.