I think it is x=asin³t, y=bcos³t.

dx = 3asin²t.cost.dt

 

If we travel along the curve from +ve y-axis towards +ve x-axis , x varies from x=0 to x=a and y varies from y=b to y=0 , i.e. , t varies from t=0 to t=pi/2.

 

Area under the curve = _[x=a]^[x=0] y.dx = _[t=0]^[t=pi/2] (bcos³t)(3asin²t.cost.dt)

 

Rest of the part is simple integration.