7. The rectangular hyperbola \(H\) has equation \(x y = c ^ { 2 }\), where \(c\) is a constant.
The point \(P \left( c t , \frac { c } { t } \right)\) is a general point on \(H\).
- Show that the tangent to \(H\) at \(P\) has equation
$$t ^ { 2 } y + x = 2 c t$$
The tangents to \(H\) at the points \(A\) and \(B\) meet at the point \(( 15 c , - c )\).
- Find, in terms of \(c\), the coordinates of \(A\) and \(B\).