| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | March |
| Marks | 4 |
| Topic | Circles |
| Type | Find centre and radius from equation |
| Difficulty | Easy -1.2 This is a straightforward application of completing the square to find circle centre and radius. Part (i) requires only rearranging to standard form (no calculation needed since k is unknown), and part (ii) involves simple algebra to find k given the radius. This is a standard textbook exercise testing basic recall of circle equation manipulation with minimal problem-solving required. |
| 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 |
|---|---|---|
| \((x + 3)^2 + (y + 2)^2 = \ldots\) with centre \((-3, 2)\) | M1, A1 | Attempt to complete the square; State correct centre www; Ignore constant term(s) |
| Answer | Marks | Guidance |
|---|---|---|
| \(13 + k = 16\), \(k = 3\) | M1, A1 | Attempt to link 9, 4, 16 and \(k\); Obtain \(k = 3\) |
**(i)**
| $(x + 3)^2 + (y + 2)^2 = \ldots$ with centre $(-3, 2)$ | M1, A1 | Attempt to complete the square; State correct centre www; Ignore constant term(s) |
**(ii)**
| $13 + k = 16$, $k = 3$ | M1, A1 | Attempt to link 9, 4, 16 and $k$; Obtain $k = 3$ |1 A circle with equation $x ^ { 2 } + y ^ { 2 } + 6 x - 4 y = k$ has a radius of 4 .\\
(i) Find the coordinates of the centre of the circle.\\
(ii) Find the value of the constant $k$.
\hfill \mbox{\textit{OCR H240/01 2018 Q1 [4]}}