I'm trying to find a set of all rational points for $\displaystyle {x^2}+{y^2}=3$. I know that if I can find a line with rational slope $\displaystyle m$ passing through point $\displaystyle (x_0,y_0)$, I can find the set but i'm having trouble finding the coordinates of the point such that they satisfy $\displaystyle {x^2}+{y^2}=3$ where they are rational numbers.

Also, how can I generalize for a circle with any radius? Finding a set of all rational points for $\displaystyle {x^2}+{y^2}=t$.