Review question

# One distance is double another; can we find a locus? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8080

## Suggestion

Given that $A$ is the point $(0,3)$ and $B$ is the point $(0,-3)$, a point $P(x,y)$ moves so that $PA=2PB$. Show that the equation of the locus of $P$ is $x^2 + y^2 +10y + 9 = 0.$

How can we work out the distances $PA$ and $PB$ (in terms of $x$ and $y$)?

In this applet, changing $\theta$ will move $P$, such that $PA = 2PB$. What shape is the locus of $P$?