June 2023 Paper 2 Q2
2 The equation of a circle is
\(x^2 - 12x + y^2 + 8y + 3 = 0\).
(a) Find the radius of the circle. [2]
(b) State the coordinates of the centre of the circle. [1]
| Scheme | Marks | AO |
|---|---|---|
| \((x \pm 6)^2\) and \((y \pm 4)^2\) | M1 | 1.1 |
| \(r = 7\) not from wrong working | A1 | 1.1 |
| [2] |
Notes
M1: completing the square twice soi
A1: NB \((x-6)^2 - 36 + (y+4)^2 - 16 + 3 = 0\) oe
allow B2 for \(r = 7\) unsupported
Alternatively
| Scheme | Marks |
|---|---|
| \(\pm 2a = -12\) oe and \(\pm 2b = 8\) oe | M1 |
| \(r = 7\) not from wrong working | A1 |
A1: NB \(r^2 = 6^2 + 4^2 - 3\)
| Scheme | Marks | AO |
|---|---|---|
| \((6, -4)\) | B1 | 1.1 |
| [1] |
Notes
B1: FT \((x \pm 6)^2 + (y \pm 4)^2\)
or FT \(\pm 2a = -12\) oe and \(\pm 2b = 8\) oe