If the line y = mx + a meets the parabola ${\mathrm{x}}^2+4\mathrm{ay}$ in two points whose abscissa are ${\mathrm{x}}_1$ and ${\mathrm{x}}_2$ then ${\mathrm{x}}_1+{\mathrm{x}}_2=0$ If

Given line $\mathrm{y}=\mathrm{mx}+\mathrm{a}$ meets parabola

$$\begin{gathered} {\mathrm{x}}^2=4\mathrm{ay} then \\ {\mathrm{x}}^2=4\mathrm{a}(\mathrm{mx}+\mathrm{a}) \\ {\mathrm{x}}^2=4\mathrm{amx}+4{\mathrm{a}}^2 \\ {\mathrm{x}}^2-4\mathrm{amx}-4{\mathrm{a}}^2=0 \end{gathered}$$

 If ${\mathrm{x}}_1, {\mathrm{x}}_2$ are roots then 

${\mathrm{x}}_1+{\mathrm{x}}_2=\frac{4\mathrm{am}}{1}=0$

$\Rightarrow \boxed{\mathrm{m}=0}$