Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The figure illustrates the circle defined by equation $x^2 + y^2 - 6x + 4y - 27 = 0$ together with the tangent to the circle at point $P\,(5, 4)$.
(a)[5]
At point $P$, the tangent to the circle cuts the $x$-axis at $A$ and the $y$-axis at $B$. Determine the area of triangle $OAB$, with $O$ as the origin.
(b)[3]
$Q$ and $R$ are also on the circle, so that $PQR$ forms an equilateral triangle. Find the exact area of triangle $PQR$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Centre correctly identified as $(3,-2)$.” …