Review question

# What is the locus of these points fixed to a rod? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5754

## Question

The ends $A$ and $B$ of a rod of fixed length move on the positive $x$ and $y$ axes respectively. $C$ is a point on $AB$, and $CD$ is perpendicular to $AB$, as shown in the figure. The lengths of $AC$, $BC$ and $CD$ are $a$, $b$ and $c$ respectively.

1. Find parametric equations for the locus of $C$.
2. Find parametric equations for the locus of $D$.
3. If $c^2=ab$ show that the locus of $D$ consists of part of a straight line and find the coordinates of the extremities of this locus.
4. Sketch the loci of $C$ and $D$ for the case $a=4$, $b=9$, $c=6$.