Question

A straight line $L$ is perpendicular to the line $5x-y=1.$ The area of the triangle formed by the line L $\&$ the coordinate axes is $5.$ Find the equation of the line.

Answer 1

$L:y=mx+c$

$L\perp$ to $5x-y=1$

$\Rightarrow m=\frac{-1}{5}$

Area $=5$ sq. units

$\Rightarrow \frac{1}{2}\times 5c\times c=5\Rightarrow c=\sqrt{2}$

$y=\frac{-x}{5}+\sqrt{2}$