Tangents Questions

Given: A circle, $2x^2+2y^2=5$ and a parabola, $y^2=4\sqrt{5}x$.Statement - I: An equation of a common tangent to these curves is $y=x+\sqrt{5}$.Statement - II: If the line $y=mx+\frac{\sqrt{5}}{m}$ ($m\ne 0$) is their common tangent, then $m$ satisfies $m^4-3m^2+2=0$.

The intercepts on $x$ -axis made by tangents to the curve $y={\int }_0^x|t|dt$, $x\in \mathbb{R}$, which are parallel to the line $y=2x$, are equal to: