Review question

# What can we deduce if the loci traced out by two points touch? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8509

## Question

A point $P(x,y)$ moves so that $OP^2=\lambda y$, where $O$ is the origin and $\lambda$ is a constant. Show that the locus of $P$ is a circle. State the coordinates of the centre of the circle and the length of its radius.

Using the same axes, find the locus of a point $Q(x',y')$ which moves so that $QR^2=\lambda' y'$, where $R$ is the fixed point $(\alpha,0)$ and $\lambda'$ is a constant.

If the two loci touch each other, and $\alpha\ne 0$, prove that $\alpha^2=\lambda\lambda'$.