Edexcel C2 — Question 8 9 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircles
TypeLine-circle intersection points
DifficultyModerate -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.
Spec1.02b 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 \(y = x + 3\).
  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  Q8 [9]}}