(a) Substitute the line equation \(y = x - 9\) into the circle equation:

\((x - 1)^2 + (x - 9 + 4)^2 = 40\)

Simplify to:

\(x^2 - 6x - 7 = 0\)

Factorize to find \(x\):

\((x + 1)(x - 7) = 0\)

Thus, \(x = -1\) or \(x = 7\).

For \(x = -1\), \(y = -1 - 9 = -10\).

For \(x = 7\), \(y = 7 - 9 = -2\).

Coordinates of intersection are \((-1, -10)\) and \((7, -2)\).

(b) The midpoint \(C\) of \(AB\) is:

\(C = \left(\frac{-1 + 7}{2}, \frac{-10 + (-2)}{2}\right) = (3, -6)\)

The radius is:

\(\sqrt{(7 - (-1))^2 + (-2 - (-10))^2} / 2 = \sqrt{32}\)

The equation of the circle with center \(C(3, -6)\) and radius \(\sqrt{32}\) is:

\((x - 3)^2 + (y + 6)^2 = 32\)