Two fixed points \(A\) and \(B\) lie in the plane, and the distance between them is \(AB=2a\), where \(a>0\).

A point \(P\) moves in the plane so that the ratio of its distances from \(A\) and \(B\) is constant: \[\frac{PA}{PB}=\lambda,\] where \(\lambda>0\).

Can you sketch the locus of the point \(P\) for different values of \(\lambda\)?

Using Cartesian coordinates, work out (the equation of) the locus of \(P\).