| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Find centre and radius from equation |
| Difficulty | Moderate -0.8 This is a straightforward circle equation question requiring completion of the square to find centre and radius. It's a standard C2 exercise with routine algebraic manipulation and direct application of the circle formula, making it easier than average but not trivial since students must remember to complete the square correctly. |
| 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 |
|---|---|---|
| (a) \(x^2 + (y-3)^2 - 9 - 7 = 0\) | M1 | |
| Centre \((0, 3)\) | A1 | |
| (b) \(x^2 + (y-3)^2 = 16\) | M1 | |
| Radius = 4 | A1 | (4 marks) |
**(a)** $x^2 + (y-3)^2 - 9 - 7 = 0$ | M1 |
Centre $(0, 3)$ | A1 |
**(b)** $x^2 + (y-3)^2 = 16$ | M1 |
Radius = 4 | A1 | (4 marks)A circle has the equation $x^2 + y^2 - 6y - 7 = 0$.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the centre of the circle. [2]
\item Find the radius of the circle. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q1 [4]}}