Since \(b \propto a^2\), we have \(b = ka^2\), where \(k\) is a non-zero constant. ___ Given that \(a\) increases in the ratio 2:3, let the initial value of \(a = 2m\) and the increased value = \(3m\) \[ \therefore\ \text{Before increase, } b = k \cdot (2m)^2 = 4km^2 \text{ and after increase, } b = k \cdot (3m)^2 = 9km^2 \] \[ \therefore\ \text{The ratio of increase in } b = \frac{4km^2}{9km^2} = 4:9 \] \[ \therefore\ b \text{ increases in the ratio } 4:9 \]