| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2025 |
| Session | February |
| Marks | 3 |
| Topic | Circles |
| Type | Find centre and radius from equation |
| Difficulty | Easy -1.2 This is a routine completing-the-square exercise to convert a circle equation to standard form. It requires only mechanical algebraic manipulation with no problem-solving or geometric insight, making it easier than average but not trivial due to the arithmetic involved. |
| Spec | 1.03e Complete the square: find centre and radius of circle |
\begin{enumerate}
\item The circle $C$ has equation
\end{enumerate}
$$x ^ { 2 } + y ^ { 2 } + 4 x - 30 y + 209 = 0$$
Find\\
(i) the coordinates of the centre of $C$,\\
(ii) the exact value of the radius of $C$.\\
coordinates of the centre of C\\
radius of $C$\\
\hfill \mbox{\textit{SPS SPS SM Pure 2025 Q1 [3]}}