| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle touching axes |
| Difficulty | Moderate -0.8 This is a straightforward C1 circles question requiring completion of the square to find the centre (routine technique), then using the tangency condition (radius equals perpendicular distance to x-axis). Both parts are standard textbook exercises with no problem-solving insight required, making it easier than average but not trivial since it involves two connected steps. |
| 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 has the equation
$$x^2 + y^2 + 8x - 4y + k = 0,$$
where $k$ is a constant.
\begin{enumerate}[label=(\roman*)]
\item Find the coordinates of the centre of the circle. [2]
\end{enumerate}
Given that the $x$-axis is a tangent to the circle,
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the value of $k$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 Q3 [5]}}