The characteristic equation of the liquid level control system is written as

\[0.006 s(s+12.5)(A s+K)+250 N=0\]

(a) For \(A=K=5\), construct the root loci of the characteristic equation as \(N\) varies from 0 to \(\infty\).

(b) For \(N=10\) and \(K=50\), construct the root loci of the characteristic equation for \(A \geq 0\).

(c) For \(A=50\) and \(N=20\), construct root loci for \(K \geq 0\).