Number Theory 1_1,Pythagorean array common frmula

Q:To give integer solutions of $a^2+b^2=c^2$

solution:
We get :$(\frac{a}{c}{)}^2+(\frac{b}{c}{)}^2=1$
let: $\frac{a}{c}=x$ $\frac{b}{c}=y$
then: just to find Rational number soluntion of $x^2+y^2=1$
Here we can fit it in a standard circle:

Then to solve: $\{\begin{array}{l}{x}^2+y^2=1\\ y=k(x-1)\end{array}$
At last we could solve the result rational number solutions