4 A curve is defined, for \(t \geqslant 0\), by the parametric equations
$$x = t ^ { 2 } , \quad y = t ^ { 3 }$$
- Show that the equation of the tangent at the point with parameter \(t\) is
$$2 y = 3 t x - t ^ { 3 } .$$
- In this question you must show detailed reasoning.
It is given that this tangent passes through the point \(A \left( \frac { 19 } { 12 } , - \frac { 15 } { 8 } \right)\) and it meets the \(x\)-axis at the point \(B\).
Find the area of triangle \(O A B\), where \(O\) is the origin.