| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Two circles intersection or tangency |
| Difficulty | Moderate -0.3 This is a straightforward C2 circle question requiring completing the square to find centre and radius (standard technique), then using distance formula and ratio to find the point of contact. While it involves multiple steps and two circles, the methods are routine textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
A circle $C$ has equation
$$x^2 + y^2 - 6x + 8y - 75 = 0.$$
\begin{enumerate}[label=(\alph*)]
\item Write down the coordinates of the centre of $C$, and calculate the radius of $C$. [3]
\end{enumerate}
A second circle has centre at the point $(15, 12)$ and radius $10$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Sketch both circles on a single diagram and find the coordinates of the point where they touch. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q3 [7]}}