- (a) On Diagram 1, sketch a graph of the curve \(C\) with equation
$$y = \frac { 6 } { x } \quad x \neq 0$$
The curve \(C\) is transformed onto the curve with equation \(y = \frac { 6 } { x - 2 } \quad x \neq 2\)
(b) Fully describe this transformation.
The curve with equation
$$y = \frac { 6 } { x - 2 } \quad x \neq 2$$
and the line with equation
$$y = k x + 7 \quad \text { where } k \text { is a constant }$$
intersect at exactly two points, \(P\) and \(Q\).
Given that the \(x\) coordinate of point \(P\) is - 4
(c) find the value of \(k\),
(d) find, using algebra, the coordinates of point \(Q\).
(Solutions relying entirely on calculator technology are not acceptable.)
\includegraphics[max width=\textwidth, alt={}]{bb21001f-fe68-4776-992d-ede1aae233d7-17_710_743_248_662}
\section*{Diagram 1}
Only use this copy of Diagram 1 if you need to redraw your graph.
\includegraphics[max width=\textwidth, alt={}, center]{bb21001f-fe68-4776-992d-ede1aae233d7-19_709_739_1802_664}
Copy of Diagram 1
(Total for Question 7 is 10 marks)