- The rectangular hyperbola \(H\) has equation \(x y = c ^ { 2 }\), where \(c\) is a positive constant.
Given that \(P \left( c t , \frac { c } { t } \right) , t \neq 0\), is a general point on \(H\),
- use calculus to show that the equation of the tangent to \(H\) at \(P\) can be written as
$$t ^ { 2 } y + x = 2 c t$$
The points \(A\) and \(B\) lie on \(H\).
The tangent to \(H\) at \(A\) and the tangent to \(H\) at \(B\) meet at the point \(\left( - \frac { 8 c } { 5 } , \frac { 3 c } { 5 } \right)\).
Given that the \(x\) coordinate of \(A\) is positive, - find, in terms of \(c\), the coordinates of \(A\) and the coordinates of \(B\).