| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2025 |
| Session | October |
| Marks | 7 |
| Topic | Circles |
| Type | Geometric properties with circles |
| Difficulty | Standard +0.8 This question requires completing the square to find the centre, calculating distances using the distance formula, and proving the right angle using Pythagoras' theorem or showing perpendicularity. It involves multiple coordinate geometry techniques and algebraic manipulation across several steps, making it moderately challenging but still within standard A-level scope. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
The circle $x^2 + y^2 + 2x - 14y + 25 = 0$ has its centre at the point C. The line $7y = x + 25$ intersects the circle at points A and B.
Prove that triangle ABC is a right-angled triangle. [7]
\hfill \mbox{\textit{SPS SPS FM 2025 Q7 [7]}}