Edexcel C2 — Question 21 9 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks9
PaperDownload PDF ↗
TopicCircles
TypeLine-circle intersection points
DifficultyModerate -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.
Spec1.02q 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 \(y = x + 3\).
  1. Write down an equation of the circle \(C\). [2]
  2. Calculate the exact coordinates of the two points where the line \(l\) intersects \(C\), giving your answers in surds. [5]
  3. Find the distance between these two points. [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]}}