OCR MEI C1 — Question 4

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
TopicCircles

4 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{12a2563e-fce4-4c82-84aa-96603a50d6ad-2_520_1115_339_565} \captionsetup{labelformat=empty} \caption{Fig. 11}
\end{figure} Fig. 11 shows the line through the points \(\mathrm { A } ( - 1,3 )\) and \(\mathrm { B } ( 5,1 )\).
  1. Find the equation of the line through \(\mathbf { A }\) and \(\mathbf { B }\).
  2. Show that the area of the triangle bounded by the axes and the line through A and B is \(\frac { 32 } { 3 }\) square units.
  3. Show that the equation of the perpendicular bisector of AB is \(y = 3 x - 4\).
  4. A circle passing through A and B has its centre on the line \(x = 3\). Find the centre of the circle and hence find the radius and equation of the circle.