| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | September |
| Marks | 5 |
| Topic | Circles |
| Type | Chord length calculation |
| Difficulty | Standard +0.3 This is a straightforward chord problem requiring: (1) finding the radius using distance formula, (2) using perpendicular distance from center to chord with Pythagoras (d² + (chord/2)² = r²), (3) identifying which of two possible y-values satisfies 'above x-axis'. All steps are standard techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
7. The circle $C$
\begin{itemize}
\item has centre $A ( 3,5 )$
\item passes through the point $B ( 8 , - 7 )$
\end{itemize}
The points $M$ and $N$ lie on $C$ such that $M N$ is a chord of $C$.\\
Given that $M N$
\begin{itemize}
\item lies above the $x$-axis
\item is parallel to the $x$-axis
\item has length $4 \sqrt { 22 }$
\end{itemize}
Find an equation for the line passing through points $M$ and $N$.\\
(5)\\
(Total for Question 7 is 5 marks)\\
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q7 [5]}}