A straight line L is perpendicular to the line 5x-y=1. The area of the triangle formed by the line L and coordinate axes is 2. The equation of the line L is ax + by + c = 0, then ${\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2$ is

Equation of the straight line L perpendicular to the line 5x-y=1 is $\mathrm{x}+5\mathrm{y}+\mathrm{k}=0$ 

Area of triangle formed with coordinate axis is 2

 $$\begin{gathered} \Rightarrow \frac{{\mathrm{c}}^2}{2\left|\mathrm{ab}\right|}=2 \\ \Rightarrow \frac{k^2}{2\left(5\right)}=2 \\ \therefore k^2=20 \\ \Rightarrow \mathrm{Equation} \mathrm{of} \mathrm{the} \mathrm{line} \mathrm{is} x+5y\pm \sqrt{20}=0 \\ \therefore a^2+b^2-c^2=1+25-20=6 \end{gathered}$$