| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | June |
| Marks | 4 |
| Topic | Circles |
| Type | Find centre and radius from equation |
| Difficulty | Moderate -0.8 This is a straightforward question requiring completion of the square to find the centre form, then using the given radius to find k. It's a standard textbook exercise with routine algebraic manipulation and no problem-solving insight required, making it easier than average. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
State $(3, 0)$ **B1**
Obtain or imply equation of the form $k \pm 9 = \pm 25$ **M1**
Obtain $k + 9 = 25$ **A1**
Obtain $k = 16$ **A1**
**[4]**5 The circle with equation $x ^ { 2 } + y ^ { 2 } - 6 x - k = 0$ has radius 5 . Find the coordinates of the centre of the circle and the value of $k$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q5 [4]}}