Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Points $P$, $Q$ and $R$ are given by the coordinates $P(-13,\ 5)$, $Q(5,\ 1)$ and $R(2,\ k)$, where $k$ is a constant. The angle $PRQ$ is a right angle.
(a)[4]
Show that one possible value of $k$ is $10$, and determine the other possible value.
(b)[5]
It is now given that $k = 10$. A circle goes through the points $P$, $Q$ and $R$. Find the equation of the tangent to the circle at $R$. Give your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Find the relevant gradient(s)” …