In coordinate geometry, the $x$ and $y$ axis are perpendicular to each other. But is there any special reason for this (other than to make it simple)? Will coordinate geometry have contradictions if the axis are at any other angle? If we take the angle between the $x$ and $y$ axis as $\theta$, will we not be able to find new theorems?
Earlier we had Eucledian geometry in which the surface was taken as a plane, and then we invented non-eucledian geometry, and we found many new theorems. Can the same thing be done to coodrdinate geometry?
Example: for $\theta=60^\circ$