$$\begin{gathered} \mathrm{If} \mathrm{a}\ne 0 \mathrm{and} \mathrm{the} \mathrm{line} 2\mathrm{bx}+3\mathrm{cy}+4\mathrm{d}=0 \mathrm{passes} \\ \mathrm{through} \mathrm{the} \mathrm{points} \mathrm{of} \mathrm{intesection} \mathrm{of} \mathrm{the} \\ \mathrm{parabola} {\mathrm{y}}^2=4\mathrm{ax} \mathrm{and} {\mathrm{x}}^2=4\mathrm{ay}, \mathrm{then} \end{gathered}$$

Point of intersection of ${\mathrm{y}}^2=4\mathrm{ax}, {\mathrm{x}}^2=4\mathrm{ay}$ are (0,0) (4a, 4a)

$2\mathrm{bx}+3\mathrm{cy}+4\mathrm{d}=0$ passes through above points

$$\begin{gathered} \begin{array}{c}\Rightarrow 4\mathrm{d}=0\\ \Rightarrow \mathrm{d}=0\end{array}\overline{)\begin{array}{c}\Rightarrow 2\mathrm{b}\left(4\mathrm{a}\right)+3\mathrm{c}\left(4\mathrm{a}\right)=0\\ \Rightarrow 4a(2\mathrm{b}+3\mathrm{c})=0\\ \Rightarrow (2\mathrm{b}+3\mathrm{c})=0\end{array}} \\ Now {\mathrm{d}}^2+{(2\mathrm{b}+3\mathrm{c})}^2=0 \end{gathered}$$