Geometry of Equations

Many ways problem

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 $\lambda>0$.
1. Can you sketch the locus of the point $P$ for different values of $\lambda$?
2. Using Cartesian coordinates, work out (the equation of) the locus of $P$.