$(\frac{1}{2},2)$ is one extremity of a focal chord of the parabola $y^2=8x.$ The coordinates of other extremity is

$y^2=8x\Rightarrow 4a=8\Rightarrow a=2\Rightarrow Focus=(2,0)$ 
If $(a{t}_1^2,2a{t}_1)=(\frac{1}{2},2)then{t}_1=\frac{1}{2}$  
If $(a{t}_2^2,2a{t}_2)$ is the other extremity then $t_1{t}_2=-1\Rightarrow t_2=-2$   
$\therefore$ Other extremity $= (8,-8)$