| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Line-circle intersection points |
| Difficulty | Moderate -0.3 This is a straightforward C2 circle question requiring standard techniques: writing a circle equation from center and radius, substituting a linear equation to find intersection points, and calculating distance. Part (b) involves solving a quadratic and working with surds, but follows a routine method with no conceptual challenges. Slightly easier than average due to the clean numbers and predictable structure. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03d Circles: equation (x-a)^2+(y-b)^2=r^2 |
A circle $C$ has centre $(3, 4)$ and radius $3\sqrt{2}$. A straight line $l$ has equation $y = x + 3$.
\begin{enumerate}[label=(\alph*)]
\item Write down an equation of the circle $C$. [2]
\item Calculate the exact coordinates of the two points where the line $l$ intersects $C$, giving your answers in surds. [5]
\item Find the distance between these two points. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q8 [9]}}