The lines \(x=0\), \(x=4\), \(y=3\) and \(y=-1\) are tangents to a circle.

(a) Find the equation of the circle.

The line \(y=2x+a\), where \(a\) is a constant, is also a tangent to the circle.

(b) Show that \(5x^2+4(a-2)x+(a-1)^2=0\), and hence find the possible values of \(a\). Give your answers in exact form.