6. The curve \(H\) has equation
$$x y = a ^ { 2 } \quad x > 0$$
where \(a\) is a positive constant.
The line with equation \(y = k x\), where \(k\) is a positive constant, intersects \(H\) at the point \(P\)
- Use calculus to determine, in terms of \(a\) and \(k\), an equation for the tangent to \(H\) at \(P\)
The tangent to \(H\) at \(P\) meets the \(x\)-axis at the point \(A\) and meets the \(y\)-axis at the point \(B\)
- Determine the coordinates of \(A\) and the coordinates of \(B\), giving your answers in terms of \(a\) and \(k\)
- Hence show that the area of triangle \(A O B\), where \(O\) is the origin, is independent of \(k\)