- The rectangular hyperbola \(H\) has equation \(x y = c ^ { 2 }\) where \(c\) is a positive constant.
The line \(l\) has equation \(x - 2 y = c\)
The points \(P\) and \(Q\) are the points of intersection of \(H\) and \(l\)
- Determine, in terms of \(c\), the coordinates of \(P\) and the coordinates of \(Q\)
The point \(R\) is the midpoint of \(P Q\)
- Show that, as \(C\) varies, the coordinates of \(R\) satisfy the equation
$$x y = - \frac { c ^ { 2 } } { a }$$
where \(a\) is a constant to be determined.