| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2019 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Find centre and radius from equation |
| Difficulty | Easy -1.2 This is a straightforward completing-the-square exercise to convert a circle equation to standard form. It requires only routine algebraic manipulation with no problem-solving or geometric insight, making it easier than average but not trivial since students must correctly complete the square for both variables. |
| 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 |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \((x \pm 4)^2\) and \((y \pm 3)^2\) seen | M1 (3.1a) | \((x+4)^2 - 4^2 + (y-3)^2 - (-3)^2 - 39 = 0\) www |
| centre is \((-4, 3)\) | A1 (1.1) | |
| [2] |
## Question 4(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $(x \pm 4)^2$ and $(y \pm 3)^2$ seen | M1 (3.1a) | $(x+4)^2 - 4^2 + (y-3)^2 - (-3)^2 - 39 = 0$ www |
| centre is $(-4, 3)$ | A1 (1.1) | |
| **[2]** | | |4 The equation of a circle is $x ^ { 2 } + y ^ { 2 } + 8 x - 6 y - 39 = 0$.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the centre of the circle.
\item Find the radius of the circle.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2019 Q4 [3]}}