The line \(L\) has equation \(y=c-mx\), with \(m>0\) and \(c>0\). It passes through the point \(R(a,b)\) and cuts the axes at the points \(P(p,0)\) and \(Q(0,q)\), where \(a\), \(b\), \(p\) and \(q\) are all positive. Find \(p\) and \(q\) in terms of \(a\), \(b\) and \(m\).

Could we draw a diagram to help us visualise the problem?

As \(L\) varies with \(R\) remaining fixed, show that the minimum value of the sum of the distances of \(P\) and \(Q\) from the origin is \((a^{\frac{1}{2}}+b^{\frac{1}{2}})^2\)

How could we find a minimum? What is varying here? Could we differentiate with respect to that?