OCR MEI C1 2013 June — Question 10 12 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2013
SessionJune
Marks12
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircles
TypeChord length calculation
DifficultyModerate -0.8 This is a straightforward C1 circle question requiring only direct application of standard formulas: reading center/radius from equation, solving simultaneous equations for axis intersections, verifying points satisfy the equation, and using midpoint/perpendicular distance formulas. All techniques are routine with no problem-solving insight needed, making it easier than average but not trivial due to the computational steps involved.
Spec1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle1.10f Distance between points: using position vectors1.10g Problem solving with vectors: in geometry

The circle \((x - 3)^2 + (y - 2)^2 = 20\) has centre C.
  1. Write down the radius of the circle and the coordinates of C. [2]
  2. Find the coordinates of the intersections of the circle with the \(x\)- and \(y\)-axes. [5]
  3. Show that the points A\((1, 6)\) and B\((7, 4)\) lie on the circle. Find the coordinates of the midpoint of AB. Find also the distance of the chord AB from the centre of the circle. [5]

The circle $(x - 3)^2 + (y - 2)^2 = 20$ has centre C.
\begin{enumerate}[label=(\roman*)]
\item Write down the radius of the circle and the coordinates of C. [2]
\item Find the coordinates of the intersections of the circle with the $x$- and $y$-axes. [5]
\item Show that the points A$(1, 6)$ and B$(7, 4)$ lie on the circle. Find the coordinates of the midpoint of AB. Find also the distance of the chord AB from the centre of the circle. [5]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C1 2013 Q10 [12]}}