| 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 -0.3 This is a straightforward circle geometry question requiring basic understanding that a circle touching the x-axis has its center directly above the point of tangency, writing the standard circle equation, and applying Pythagoras to a radius-tangent-chord triangle. All parts use standard techniques with no novel problem-solving required, making it slightly easier than average for A-level. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03f Circle properties: angles, chords, tangents |
Figure 1
\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]}}