Sketch the form of the curve \(27y^2=x^3\), and find the equation of the tangent at the point \(P(12,8)\) on the curve.

Verify this tangent cuts the curve again at the point \(Q(3,-1)\).

If \(O\) is the origin, find by integration the area enclosed by the arcs \(OP\), \(OQ\) of the curve and the line \(PQ\). [Integration with respect to \(y\) is recommended.]