Think about eqn 1. This is satisfied by all the points on a circle of radius 1. You can think of (a,b) as a 2 component vector of magnitude 1 pointing to some point on the circle.
You can reach the same conclusion about (c,d) from eqn.3
Eqn 2 tells you that (a,b) is perpendicular to (c,d) because the dot product is zero.
The net effect is that all solutions look like the hour hand and minute hand at 3:00, but with some arbitrary rotation.