The length of chord of parabola  $x^2=4y$ having the equation, $x-\sqrt{2}y+4\sqrt{2}=0$  is

 $x^2=4y,x-\sqrt{2}y+4\sqrt{2}=0$
Eliminate(y)  $\Rightarrow \sqrt{2}{x}^2-4x-16\sqrt{2}=0$
$x_1+x_2=2\sqrt{2},x_1{x}_2=-16$
Similarly eliminate(x),  $2y^2-20y+32=0,y_1+y_2=10,y_1{y}_2=16$
$\therefore$Length  $AB=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$