The distance from the center of the circle to the two coordinate axes is equal.

∴x=y or x=-y

The center of the circle is 5x-3y=8.

∴x=y, then x=y=4, x=-y, then x= 1, y=- 1.

The center of the circle is (4,4) or (1,-1).

∴ If the center of the circle is (4,4), then r=4.

If the center of the circle is (1,-1), there is r= 1.

∴ The standard equation of a circle tangent to two coordinates is:

(x-4)^2+(y-4)^2= 16

(x- 1)^2+(y+ 1)^2= 1