Question

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

Answer 1

Solution -

Slope of line $=\frac{-1}{5}$

Line $y=\frac{-1}{5}x+c$

cuts x-axis at $(5c,0)$

cuts y-axis at $(0,c)$

Area $=\frac{1}{2}5c\times c=5$

$c^2=2\Rightarrow c=\pm \sqrt{2}$

Line $\to x+y=\pm 5\sqrt{2}$