what is the maximum height from vent to cooktop

What kind of ventilation is this? Forced (mechanical/fan) or natural?  Chapter 15 of the International Residential Code described ventilation of bathrooms and kitchens and it's mostly concerned with the amount of air removed/replaced, duct material and where the exhaust air is going. The actual location of the vent relative to the stove is not described in any way.

Is this a hooded vent, by the way? The further away from the surface the less effective the ventilation. If there's a hood I'd say 32-36 inches away from the cooktop is best and many manufacturers have minimum heights prescribed (24"-30", in that range) as opposed to maximum.

To answer this better would require knowing more details about your kitchen: gas or electrical range, hood or not, size of room, brands / model numbers of all equipment involved is also very useful.