If hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$intersects parabola $y=b{x}^2,$ then ${\left[a\right]}^{ }\in$------(where$\left[ \right]$is GIF) 

$x^2=\frac{y}{b}$  in Hyperbola $\Rightarrow a^2{y}^2-by+a^2{b}^2=0\left(△\ge 0\right)$
$$\begin{gathered} \Rightarrow b^2-4b^2{a}^4\ge 0 \\ \Rightarrow 4a^4-1\le 0 \\ \Rightarrow a^2-\frac{1}{2}\le 0 \end{gathered}$$

Now  $△\ge 0\Rightarrow -\frac{1}{\sqrt{2}}\le a\le \frac{1}{\sqrt{2}}\Rightarrow \left[a\right]=-1,0$

$\mathrm{but} \left[\mathrm{a}\right]=-1 \mathrm{is} \mathrm{not} \mathrm{possible}$