# Locus

• If we have a line $l$ and a point $P$, a parabola is the locus of all points $S$ such that $SP=$ the distance from $S$ to $l$.
• If we have two points A and B, an ellipse is the locus of all points $S$ such that $SA+SB$ is equal to a given constant.
• Given two points $A$ and $B$ and a constant $k$, the locus of all points $P$ that satisfy $\frac{PA}{PB} = k$ is a circle (sometimes called an Apollonius circle).