| 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 Part (a) is a standard completing-the-square exercise to find centre and radius from general circle equation—routine C2 content. Part (b) requires recognizing the circles touch externally, finding the distance between centres, and using ratio to locate the point of contact, which involves slightly more problem-solving than pure recall but remains a typical textbook question with clear methodology. |
| 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 Q4 [7]}}