| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2021 |
| Session | November |
| Marks | 10 |
| Topic | Circles |
| Type | Tangent equation at a known point on circle |
| Difficulty | Moderate -0.8 This is a straightforward circle question with standard bookwork parts. Parts (a)(i) and (a)(ii) are direct reading from the equation (1 mark each). Part (b) is a routine tangent calculation using perpendicular gradients (4 marks but standard method). Part (c) uses Pythagoras on the right-angled triangle formed by radius, tangent, and line from centre to external point - a common textbook exercise. All parts follow predictable patterns with no novel problem-solving required. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle1.07m Tangents and normals: gradient and equations |
8.
The circle with equation $( x - 7 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 5$ has centre $C$.
\begin{enumerate}[label=(\alph*)]
\item (i) Write down the radius of the circle.\\[0pt]
[1 mark]\\
(a) (ii) Write down the coordinates of $C$.\\[0pt]
[1 mark]
\item The point $P ( 5 , - 1 )$ lies on the circle.
Find the equation of the tangent to the circle at $P$, giving your answer in the form $y = m x + c$\\[0pt]
[4 marks]
\item The point $Q ( 3,3 )$ lies outside the circle and the point $T$ lies on the circle such that $Q T$ is a tangent to the circle. Find the length of $Q T$.\\[0pt]
[4 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2021 Q8 [10]}}