The length of the radius is equal to the distance from the center of the circle to the straight line x-y- 1=0.

So the radius =|a+2a- 1|/ radical number 2=|3a- 1|/ radical number 2.

So the equation of circle: (x-a) 2+(y+2a) 2 = (3a- 1) 2/2.

Because the circle passes through the point (2,-1)

so(2-a)2+(2a- 1)2 =(3a- 1)2/2。

8-8a-2a^2+8a^2-8a+2=9a^2-6a+ 1

3a^2+ 10a-9=0

△= 100+ 108=208

A = (- 10 root number 208)/6 = (2 root numbers 13-5)/3.