If the circle C passes through (2, - 1) and is tangent to the line x-y-1 = 0, and the center of the circle is on the line y = - 2x, then the standard equation of the circle C is

If the circle C passes through (2, - 1) and is tangent to the line x-y-1 = 0, and the center of the circle is on the line y = - 2x, then the standard equation of the circle C is

Let the center of the circle be C (m, - 2m), and the distance from C to point a (2, - 1), which is equal to the distance to the straight line L: x-y-1 = 0, be the radius of circle C RR ^ 2 = (m-2) ^ 2 + (- 2m + 1) ^ 2 = [M - (- 2m) - 1] ^ 2 / [1 ^ 2 + (- 1) ^ 2], and then (m-2) ^ 2 + (2m-1) ^ 2 = 1 / 2 * (3m-1) ^ 2. When m = 9 or M = 1m = 9, C (9, - 18), R ^ 2 = 338