### Geometry of Equations

Many ways problem

# The circle of Apollonius... coordinate edition Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Problem 1

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 $P$.