If $\frac{a}{\sqrt{bc}}-2=\sqrt{\frac{b}{c}}+\sqrt{\frac{c}{b}}a,b,c>0thenfamilyoflines\sqrt{a}x+\sqrt{b}y+\sqrt{c}=0$ passes through the point

 $\begin{array}{l}\frac{a}{\sqrt{bc}}-2=\sqrt{\frac{b}{c}}+\sqrt{\frac{c}{b}}\\ \Rightarrow \frac{a-2\sqrt{bc}}{\cancel{\sqrt{bc}}}=\frac{b+c}{\cancel{\sqrt{bc}}}\Rightarrow b+c+2\sqrt{b}\sqrt{c}\\ \Rightarrow {\left(\sqrt{b}+\sqrt{c}\right)}^2-{\left(\sqrt{a}\right)}^2=0\\ \Rightarrow \left(\sqrt{b}+\sqrt{c}+\sqrt{a}\right)\left(\sqrt{b}+\sqrt{c}-\sqrt{a}\right)=0\\ \therefore \sqrt{a}+\sqrt{b}+\sqrt{c}=0and\sqrt{a}-\sqrt{b}-\sqrt{c}=0\\ \Rightarrow \sqrt{a}\left(1\right)+\sqrt{b}\left(1\right)+\sqrt{c}=0\\ Comparingwith\sqrt{a}x+\sqrt{b}y+\sqrt{c}=0\\ x=1,y=1,\therefore \left(x,y\right)=\left(1,1\right)\end{array}$