8. The rectangular hyperbola \(H\) has equation \(x y = c ^ { 2 }\), where \(c\) is a positive constant.
The point \(P \left( c t , \frac { c } { t } \right) , t \neq 0\), is a general point on \(H\).
- Show that an equation for the tangent to \(H\) at \(P\) is
$$x + t ^ { 2 } y = 2 c t$$
The tangent to \(H\) at the point \(P\) meets the \(x\)-axis at the point \(A\) and the \(y\)-axis at the point \(B\). Given that the area of the triangle \(O A B\), where \(O\) is the origin, is 36 ,
- find the exact value of \(c\), expressing your answer in the form \(k \sqrt { } 2\), where \(k\) is an integer.