Edexcel C1 — Question 5

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
TopicStraight Lines & Coordinate Geometry

5. \section*{Figure 1}
\includegraphics[max width=\textwidth, alt={}]{3d5491ef-91cf-4ba9-b00b-cd326d51e6e1-3_686_1066_276_559}
Figure 1 shows the curve with equation \(y ^ { 2 } = 4 ( x - 2 )\) and the line with equation \(2 x - 3 y = 12\). The curve crosses the \(x\)-axis at the point \(A\), and the line intersects the curve at the points \(P\) and \(Q\).
  1. Write down the coordinates of \(A\).
  2. Find, using algebra, the coordinates of \(P\) and \(Q\).
  3. Show that \(\angle P A Q\) is a right angle. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{3d5491ef-91cf-4ba9-b00b-cd326d51e6e1-4_646_1043_291_336}
    \end{figure} The points \(A ( 3,0 )\) and \(B ( 0,4 )\) are two vertices of the rectangle \(A B C D\), as shown in Fig. 2.