If the tangent to the curve $y=1-x^2$ at $x=\alpha$, where $0<\alpha <1$, meets the axes at $P$ and $Q.$ As $\alpha$ varies, the minimum value of the area of the triangle $OPQ$ is $k$ times the area bounded by the axes and the part of the curve for which $0<x<1$, then $k$ is equal to -

Let $f\left(x\right)=\left|x\right|-2$ and $g\left(x\right)=\left|f\left(x\right)\right|$. Now area bounded by $x-$axis and $f\left(x\right)$ is $A_1$ and area bounded by $x$-axis and $g\left(x\right)$ is $A_2$ then-

Statement I: The area bounded by the curves $y=x^2-3$ and $y=kx+2$, is least if  $k=0.$

Statement II: The area bounded by the curves $y=x^2-3$ and $y=kx+2$ is $\sqrt{k^2+20}.$