Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
A circle is described by the equation $x^2 + y^2 + px + 2y + q = 0$, where $p$ and $q$ are constants.
(a)[2]
Rewrite the equation in the form $(x - a)^2 + (y - b)^2 = r^2$, with $a$ stated in terms of $p$ and $r^2$ stated in terms of $p$ and $q$.
(b(i))[3]
The line $x + 2y = 10$ is tangent to the circle at $A(4, 3)$. Determine the equation of the normal to the circle at $A$.
(b(ii))[5]
Determine the values of $p$ and $q$.
(ii)[5]
Determine the values of $p$ and $q$.
Worked solution & mark scheme
This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Circle equation stated correctly with centre $(-\frac12p,-1)$” …