Which of these models of the solar system first proved that the sun is at one of the foci of earth's elliptical orbit? kepler model ptolemic model copernicus model brahe model

Kepler was the first scholar to hypothesize and theorize that concept.

BUT ... a model doesn't 'prove' anything, and a theory is never 'proved'.

Kepler's model, when combined with Newton's universal gravitation, 
simply explains everything we see in the solar system almost perfectly, 
makes predictions that check out almost perfectly, and when used to 
navigate spacecraft, the spacecraft go exactly where we want them to go.

If Newton's gravity is correct, then the result of it HAS TO BE Kepler's model.
But still, Kepler's model and Newton's gravity are still "only theories".  Neither
has been proved.) 

(The greatest scientists have been trying to prove them wrong for 300 years.
They haven't been successful yet, but they're still trying.  Real science is not
attempts to prove that certain ideas are right.  It's more of an attempt to prove
that certain ideas are wrong.)