| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Line-circle intersection points |
| Difficulty | Moderate -0.3 This is a straightforward C2 circles question with standard techniques: writing circle equation from centre/radius, substituting a linear equation to find intersections (solving a quadratic), and finding distance between points. All methods are routine with no novel insight required, making it slightly easier than average but still requiring careful algebraic manipulation across multiple steps. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.03d 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 Q21 [9]}}