| Exam Board | SPS |
|---|
| Module | SPS SM Pure (SPS SM Pure) |
|---|
| Year | 2023 |
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| Session | September |
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| Topic | Circles |
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3.
$$x ^ { 2 } + y ^ { 2 } - 2 x - 2 y = 8$$
The circle with the above equation has radius \(r\) and has its centre at the point \(C\).
a) Determine the value of \(r\) and the coordinates of \(C\).
The point \(P ( 4,2 )\) lies on the circle.
b) Show that an equation of the tangent to the circle at \(P\) is
$$y = 14 - 3 x$$
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