Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The coordinates of points $A$, $B$ and $C$ are $A(5,-2)$, $B(10,3)$ and $C(2p,p)$, with $p$ as a constant.
(a)[3]
Because $AC$ and $BC$ are the same length, determine the value of $p$.
(b(i))[4]
It is now stated instead that $AC$ is perpendicular to $BC$, and that $p$ is an integer. Determine $p$.
(b(ii))[4]
Find the equation of the circle through $A$, $B$ and $C$, and give your answer in the form $x^2 + y^2 + ax + by + c = 0$, where $a$, $b$ and $c$ are constants.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Sets up the correct equation using distances” …