I am confused by the following example about solving quasilinear first order PDEs.
For the part I circled, the solution is just x^2 + y^2 = k where k is an arbitrary constant. To parametrize it in terms of t, can't we just put x = a cos(t), y = a sin(t) ? Here we only have one arbitrary constant a.
But in the example, they used a weird parametrization of a circle that includes TWO arbitary constants a and b. So my point is: why introduce another extra arbitrary constant when it is completely unnecessary to do so?
Can someone please explain why it is absolutely necessary to parametrize the circle in the way they do?
Any help is greatly appreciated!
[note: also under discussion in S.O.S. math cyberboard]