Circle touching both axes with centre on x-2y=3

[zorro]

Homework Statement

Find the equation of the circle which touches the axes and whose centre lies on the line x-2y=3

Homework Equations

The Attempt at a Solution

The given line passes through 1st, 3rd and 4th quadrants.
So the centre of the circle may lie in any of these i.e. it can be of the form (a,a) (a,-a) (-a,-a).
But my book considers only (a,a) (a,-a) for finding the equation of circles.

 

[Mentallic]

for the line $$y=x/2-3/2$$ even though it passes through the first quadrant, it doesn't intersect the line y=x, x>0 so there cannot exist a circle with centre on that line which touches both x and y axes.

 

[zorro]

Thanks a lot!

 

[Mentallic]

No problem You don't even have to consider which quadrants the line is in, just start solving for that line and the lines y=x and y=-x.