If the form of a conic is

ax˛ + 2hxy + by˛ + 2fx + 2gy + k = 0

and to rotate the axis from (x,y) to (X,Y) you must use

x = XcosT - YsinT

y = XsinT + YcosT

how can I show that to get rid of the xy coefficient, T must be found using

tan(2T) = 2h / (a-b)???