The equation of a circle is \(x^2 + y^2 - 4x + 6y - 77 = 0\).

(a) Find the \(x\)-coordinates of the points \(A\) and \(B\) where the circle intersects the \(x\)-axis.

(b) Find the point of intersection of the tangents to the circle at \(A\) and \(B\).