- The hyperbola \(H\) has equation \(x y = c ^ { 2 }\) where \(c\) is a positive constant.
The point \(P \left( c t , \frac { c } { t } \right)\), where \(t > 0\), lies on \(H\).
The tangent to \(H\) at \(P\) meets the \(x\)-axis at the point \(A\) and meets the \(y\)-axis at the point \(B\).
- Determine, in terms of \(c\) and \(t\),
- the coordinates of \(A\),
- the coordinates of \(B\).
Given that the area of triangle \(A O B\), where \(O\) is the origin, is 90 square units,
- determine the value of \(c\), giving your answer as a simplified surd.