The point of interaction is $ay^2 = x^3, by = x$

$ay^2 = (by)^3$

$b^3y^3 - ay^2 = 0 \Rightarrow y^2(b^3y-a)=0$

$y = \frac{a}{b^3}, x = \frac{a}{b^2}$

$\therefore$ the point of intersection is $\Big(\frac{a}{b^2}, \frac{a}{b^3}\Big)$

The lamina is the area OBA on the curve OBA $y=\frac{x^{3/2}}{\sqrt{a}}$ and on the line …