Let (x, y) and (X, Y) be the old and the new coordinates, respectively. Therefore
x = X cos (-45°) - Y sin(-45°) = X +Y/√2
and y = X sin(-45°) + Y cos(-45°) = -X + Y/√2
Now,
When we deal with hyperbola (conic section), we see that x2 -y2 = a2 the standard equation of rectangular hyperbola and xy = c2 is the rectangular hyperbola in the simplest form