Number Theory 1_1,Pythagorean array common frmula

Q:To give integer solutions of $a^2+b^2=c^2$a2+b2=c2

solution:
We get :$(\frac{a}{c})^2+(\frac{b}{c})^2=1$(ca​)2+(cb​)2=1
let: $\frac{a}{c}=x$ca​=x $\frac{b}{c}=y$cb​=y
then: just to find Rational number soluntion of $x^2+y^2=1$x2+y2=1
Here we can fit it in a standard circle:

Then to solve: $\begin{cases} x^2+y^2=1 \\ y=k(x-1) \end{cases}${x2+y2=1y=k(x−1)​
At last we could solve the result rational number solutions