Review question

# What's the locus of the intersection of these variable lines? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5255

## Question

The line $x+y=t$ meets the line $y=tx$ at the point $P$. Find the coordinates of $P$ in terms of $t$. Hence, or otherwise, show that the equation of the locus of $P$ as $t$ varies is $x^2+xy-y=0$. At the point on the locus where $x=3$, find the value of $y$ and the value of $t$.