SPS SPS SM Pure 2025 February — Question 1 3 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2025
SessionFebruary
Marks3
TopicCircles
TypeFind centre and radius from equation
DifficultyEasy -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.
Spec1.03e Complete the square: find centre and radius of circle

  1. The circle \(C\) has equation
$$x ^ { 2 } + y ^ { 2 } + 4 x - 30 y + 209 = 0$$ Find
  1. the coordinates of the centre of \(C\),
  2. the exact value of the radius of \(C\).
    coordinates of the centre of C
    radius of \(C\)

\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]}}