The length of the subnormal to the curve ${\mathrm{x}}^2+4\mathrm{ay}$ at (4a, 4a) is

$\begin{array}{rcl}{\mathrm{x}}^2& =& 4\mathrm{ay}\\ 4\mathrm{a}\frac{\mathrm{dy}}{\mathrm{dx}}& =& 2\mathrm{x}\\ \mathrm{m}& =& {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}_{(\mathrm{a}, 4\mathrm{a})}\\ & =& \frac{2\left(4\mathrm{a}\right)}{4\mathrm{a}}=2\end{array}$

Length of sub normal $=\left|{\mathrm{y}}_1 \mathrm{m}\right|$

                                       $$\begin{gathered} =4\mathrm{a} \left(2\right) \\ =8\mathrm{a} \end{gathered}$$