| Exam Board | SPS |
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | October |
| Topic | Circles |
8. The equation of a circle is \(x ^ { 2 } + y ^ { 2 } + 6 x - 2 y - 10 = 0\).
i. Find the centre and radius of the circle.
ii. Find the coordinates of any points where the line \(y = 2 x - 3\) meets the circle \(x ^ { 2 } + y ^ { 2 } + 6 x - 2 y - 10 = 0\).
iii. State what can be deduced from the answer to part ii. about the line \(y = 2 x - 3\) and the circle \(x ^ { 2 } + y ^ { 2 } + 6 x - 2 y - 10 = 0\).
iv. The point \(A ( - 1,5 )\) lies on the circumference of the circle \(x ^ { 2 } + y ^ { 2 } + 6 x - 2 y - 10 = 0\). Given that \(A B\) is a diameter of the circle, find the coordinates of \(B\).