Show that the circle x^2+y^2-2ax-2ay+a^2=0 touches both the coordinate axes.
Given equation is
x2 + y2 -2ax -2ay +a2 =0
Now, adding and subtracting a2 from the above equation,
⇒ x2 + a2 - 2ax + y2 - 2ay + a2 - a2 = 0
⇒ (x - a)2 + (y - a)2 = a2
Clearly we can see from above example when x = 0, y = a and when x = a, y = 0.
Thus it touches x and y axes at (a,0) and (0,a).