The length of the focal chord of the parabola  $x^2=4y$  which touches the hyperbola  $x^2-4y^2=1$is

Let  $\left(2t_1,t_1^2\right)and\left(2t_2,t_2^2\right)$  be extremities of focal chord  $\Rightarrow t_1{t}_2=-1$

Equation of focal chord;  $x\left(t_1+t_2\right)-2y+2=0$  and the line   $y=mx+\sqrt{m^2-\frac{1}{4}}$ tangent to hyperbola passes through (0, 1) 

$\Rightarrow m=\pm \frac{\sqrt{5}}{2}=t_1+t_2$

$\Rightarrow$Length of the focal chord = 9