| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Find centre and radius from equation |
| Difficulty | Moderate -0.8 This is a straightforward C1 circles question requiring completion of the square to find centre/radius (standard technique) and using the diameter property that the centre is the midpoint of AB (simple coordinate geometry). Both parts are routine textbook exercises with no problem-solving insight needed, making it easier than average but not trivial since it requires correct algebraic manipulation. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
| Answer | Marks | Guidance |
|---|---|---|
| Marks: B1 | M1 | A1 [3] |
| Guidance: | \((y \pm 4)^2 - 4^2\) seen (or implied by correct answer) | Do not allow A mark from \((y - 4)^2\) |
| Answer | Marks |
|---|---|
| Marks: B1FT | B1FT [2] |
| Guidance: FT through centre given in (i) | FT through centre given in (i) |
## (i)
**Answer:** Centre $(0, -4)$; $x^2 + (y + 4)^2 - 16 - 24 = 0$; Radius $= \sqrt{40}$
**Marks:** B1 | M1 | A1 [3]
**Guidance:** | $(y \pm 4)^2 - 4^2$ seen (or implied by correct answer) | Do not allow A mark from $(y - 4)^2$
**Additional notes:** Or attempt at $r^2 = f^2 + g^2 - c$; A0 for $\pm\sqrt{40}$
## (ii)
**Answer:** $(-2, -10)$
**Marks:** B1FT | B1FT [2]
**Guidance:** FT through centre given in (i) | FT through centre given in (i)
**Additional notes:** i.e. (their $2x - 2$, their $2y - 2$); Apply same scheme if equation of diameter found and attempt to solve simultaneously; no marks until a correct value of $x/y$ found.
---A circle $C$ has equation $x^2 + y^2 + 8y - 24 = 0$.
\begin{enumerate}[label=(\roman*)]
\item Find the centre and radius of the circle. [3]
\item The point $A(2, 2)$ lies on the circumference of $C$. Given that $AB$ is a diameter of the circle, find the coordinates of $B$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2013 Q6 [5]}}