| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle from diameter endpoints |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing standard circle techniques: midpoint formula for the centre, distance formula for radius, point verification by substitution, and perpendicular gradient for tangent. All parts are routine applications of formulas with no problem-solving insight required, making it easier than average but not trivial due to the computational steps involved. |
| 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 |
9. The points $A$ and $B$ have coordinates $( - 2,11 )$ and $( 8,1 )$ respectively.
Given that $A B$ is a diameter of the circle $C$,
\begin{enumerate}[label=(\alph*)]
\item show that the centre of $C$ has coordinates $( 3,6 )$,
\item find an equation for $C$.
\item Verify that the point $( 10,7 )$ lies on $C$.
\item Find an equation of the tangent to $C$ at the point (10, 7), giving your answer in the form $y = m x + c$, where $m$ and $c$ are constants.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2011 Q9 [10]}}