| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | September |
| Marks | 7 |
| Topic | Circles |
| Type | Circle from diameter endpoints |
| Difficulty | Moderate -0.8 This is a straightforward multi-part circle question requiring standard techniques: finding radius using distance formula, using diameter properties (midpoint), and finding tangent perpendicular to radius. All parts are routine applications of well-practiced methods with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle1.03f Circle properties: angles, chords, tangents |
3. A circle with centre $C ( 5 , - 3 )$ passes through the point $A ( - 2,1 )$.
\begin{enumerate}[label=(\alph*)]
\item Find the equation of the circle in the form
$$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = k$$
\item Given that $A B$ is a diameter of the circle, find the coordinates of the point $B$.
\item Find an equation of the tangent to the circle at the point $A$, giving your answer in the form $p x + q y + r = 0$, where $p , q$ and $r$ are integers.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q3 [7]}}