Find the equation of a circle. If a circle which center is on the straight line $x-2y+3=0$ cuts both the x-axis and the y-axis, what is the equation of the circle? 
ANSWER: $x^2+y^2-6x-6y+9=0$
This is rather a straightforward question but I don't know how to start...some hints would be very much appreciated.

HINT:
Let $\alpha,\beta$ be the center of the circle with radius $=r$
$\implies \alpha-2\beta=3\iff \alpha=2\beta-3$ 
Assuming 'cuts' means 'touches', the axes are tangents of the circle.
So, the perpendicular distance(s) of each axis from the center$(2\beta-3,\beta)$ equals to the radius$(=r)$ 
Do you know the equation of the axes and
how to calculate the perpendicular distance of a straight line from a given point
