Review question

# Can we show that this point moves on a circle? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6234

## Suggestion

1. The point $A$ has coordinates $(5,16)$ and the point $B$ has coordinates $(-4,4)$. The variable point $P$ has coordinates $(x,y)$ and moves on a path such that $AP = 2BP$. Show that the Cartesian equation of the path of $P$ is $(x + 7)^2 + y^2 = 100.$

In this applet, as you move $P$, the two bars show the relative sizes of $AP$ and $2\times BP$. When are they equal?

Can we find the lengths $AP$ and $BP$ in terms of $x$ and $y$?

… Given that the path of $Q$ is the same as the path of $P$

What do we know about the equations of the paths of $P$ and $Q$ in this case? Must they be the same?