| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle through three points using right angle in semicircle |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard C1 circle techniques: showing perpendicularity using gradients, finding the centre as the midpoint of a diameter (using the right-angle-in-semicircle property), and converting to general form. All parts follow routine procedures with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.03b Straight lines: parallel and perpendicular relationships1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
The points $P$, $Q$ and $R$ have coordinates $(-5, 2)$, $(-3, 8)$ and $(9, 4)$ respectively.
\begin{enumerate}[label=(\roman*)]
\item Show that $\angle PQR = 90°$. [4]
\end{enumerate}
Given that $P$, $Q$ and $R$ all lie on a circle,
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item find the coordinates of the centre of the circle, [3]
\item show that the equation of the circle can be written in the form
$$x^2 + y^2 - 4x - 6y = k,$$
where $k$ is an integer to be found. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 Q6 [10]}}