Is part of a circle lying on first quadrant?

Question

I have circle $ C: (x-x_0)^2+(y-y_0)^2\leq r^2$ with center $(x_0,y_0)$ and radius $r$.

I want to find out in exactly what quadrants the circle lies. Is there a condition with this functionality?

i.e if the cirlce lies exclusively in the first quadrant what condition should hold truth?

i.e If the circle lies in first and second quadrant what condition should hold truth?

Answer 1

Just note that $x_0 > r$ would imply the circle was entirely to the right of the $y$-axis, similarly $y_0 > r$ would imply the circle was entirely to the above the $x$-axis. Extend this logic and the solution falls out.