June 2024 Paper 1 Q6
6 Points \(A\ (-12, 1)\) and \(B\ (12, -1)\) lie on a circle.
\(AB\) is a diameter of the circle.
Work out the equation of the circle. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(x^2 + y^2 = 145\) | B3 | B2 centre (0, 0) and (radius \(=\)) \(\sqrt{145}\) or centre (0, 0) and (radius\(^2 =\)) 145 or \((x - 0)^2 + (y - 0)^2 = 145\) or \(x^2 + y^2 = \sqrt{145}\) B1 \(x^2 + y^2 = k\) or \((x - 0)^2 + (y - 0)^2 = k\) or \((x + \ldots)^2 + (y + \ldots)^2 = 145\) or centre (0, 0) or (radius \(=\)) \(\sqrt{145}\) or (radius \(=\)) \(\sqrt{12^2 + 1^2}\) or (radius\(^2 =\)) 145 or \(12^2 + 1^2\) or (radius \(=\)) \(\dfrac{\sqrt{580}}{2}\) or (radius\(^2 =\)) \(\dfrac{580}{4}\) |
Additional guidance
| \(k\) is a positive number (not 0) | |
| Penalise further incorrect working | |
| (0, 0) needs to be stated as centre and not just shown on a diagram nor stated as a midpoint | |
| No marks for finding diameter on its own |