Review question

# A point $Y$ moves to define a point $P$ — can we find the locus of $P\,$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6583

## Suggestion

$X$ is a fixed point $(3,0)$, $Y$ is the point $(0,a)$. A line is drawn through $Y$ and perpendicular to $XY$, meeting the $x$-axis at $Q$. On this line a point $P$ is taken so that $Y$ is the mid-point of $QP$. Find the coordinates of $P$.

There is a lot of information here given in a verbal form. It is always useful to sketch the situation to make sense of what is being asked.

Find the equation of the locus of $P$ for varying values of $a$.

How are the coordinates of $P$ related to each other?