Let a line y=m x(m>0) intersect the parabola

Let the coordinates of $P=P\left(t^{2}, t\right)$

Tangent at $P\left(t^{2}, t\right)$ is $t y=\frac{x+t^{2}}{2}$

$\Rightarrow \quad 2 t y=x+t^{2}$

$Q\left(-t^{2}, 0\right), O(0,0)$

$\therefore \quad$ Area of $\Delta O P Q=\frac{1}{2}\left|\begin{array}{ccc}0 & 0 & 1 \\ t^{2} & t & 1 \\ -t^{2} & 0 & 1\end{array}\right|=4$

$\Rightarrow|t|^{3}=8$

$t=\pm 2(t>0)$

$\therefore \quad 4 y=x+4$ is a tangent

$\therefore \quad P$ is $(4,2)$

Now, $y=m x \quad \therefore m=\frac{1}{2}$