The equation of a line is \(y = mx + c\), where \(m\) and \(c\) are constants, and the equation of a curve is \(xy = 16\).

(a) Given that the line is a tangent to the curve, express \(m\) in terms of \(c\).

(b) Given instead that \(m = -4\), find the set of values of \(c\) for which the line intersects the curve at two distinct points.