Let end points of normal are $\left({{\mathrm{at}}_{ }}^2, 2{\mathrm{at}}_{ }\right)$ and $\left({{\mathrm{at}}_1}^2, 2{\mathrm{at}}_1\right)$

$\Rightarrow t_1=-t-\frac{2}{t}$

Normal subtend a right angle at vertex then $\mathrm{t}=\pm \sqrt{2}$

$\Rightarrow t_1=\pm 2\sqrt{2}$

End points of normal chord are $(2a,\pm 2\sqrt{2}a) and (8a,\pm 4\sqrt{2}a)$

length of normal chord= $\sqrt{36a^2+72a^2}=6\sqrt{3}a$