| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle touching axes |
| Difficulty | Moderate -0.8 This is a straightforward circle geometry question requiring basic understanding of tangency conditions and Pythagoras' theorem. Parts (a) and (b) involve simple geometric reasoning to find the centre and write the circle equation. Part (c) uses the standard right-angled triangle formed by radius, tangent, and line from centre to external point—a routine technique taught in C2 with no novel problem-solving required. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^2 |
\includegraphics{figure_1}
The circle $C$, with centre $(a, b)$ and radius $5$, touches the $x$-axis at $(4, 0)$, as shown in Fig. 1.
\begin{enumerate}[label=(\alph*)]
\item Write down the value of $a$ and the value of $b$. [1]
\item Find a cartesian equation of $C$. [2]
\end{enumerate}
A tangent to the circle, drawn from the point $P(8, 17)$, touches the circle at $T$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find, to 3 significant figures, the length of $PT$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q2 [6]}}