| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Point position relative to circle |
| Difficulty | Standard +0.8 This question requires completing the square to find the circle's center and radius, then using the geometric insight that max/min distances from origin occur along the line through O and the center. While the technique is standard, it requires multiple steps (algebraic manipulation, geometric visualization, and calculation) and some problem-solving insight rather than pure recall, placing it moderately above average difficulty. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
1.A point $P$ lies on the curve with equation
$$x ^ { 2 } + y ^ { 2 } - 6 x + 8 y = 24$$
Find the greatest and least possible values of the length $O P$ ,where $O$ is the origin.
\hfill \mbox{\textit{Edexcel AEA 2005 Q1 [6]}}