Find the radii of the two circles which pass through the point $(16,2)$ and touch both axes How can I find the radii of the two circles which pass through the point $(16,2)$ and touch both the axes? I've only ever seen demonstrations using three normal co-ordinates; or two normal co-ordinates and touching 1 axis. 
I tried something along the lines of:
$$
x^2 + y^2 + 2gx+2fx+c=0 \\
260 + 32g+4f + c = 0
$$
And since we know it also meets the co-ordinates $(0,y)$ and $(x,0)$:
$$
x^2 + 2gx = -c = y^2+2fy
$$
But I'm not sure if this is a valid approach. Plugging the latter into the former doesn't seem to go anywhere...

Hint:
Circles which touch both axes in the first quadrant would be of form $(x-a)^2+(y-a)^2=a^2$ (why?).  You want this to pass through $(16, 2)$, so that helps find possible values of $a$.
