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  4. If a line L is perpendicular to the line 5x - y = 1, and the area of the triangle formed by the line L and the coordinate axes is 5, then the distance of line L from the line x + by = 0 is :

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Q. If a line $L$ is perpendicular to the line $5x - y = 1$, and the area of the triangle formed by the line $L$ and the coordinate axes is $5$, then the distance of line $L$ from the line $x + by = 0$ is :

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Solution:

Equation = of line L is
$x+5 y+c=0$
$\frac{c^{2}}{2|1 \times 5|}=5$
$\Rightarrow c=\pm 5 \sqrt{2}$
$\therefore $ Eq of line $L$ is
$x+5 y \pm \,5 \sqrt{2}=0$
Its distance from $x+5 y=0$ is $\frac{5}{\sqrt{13}}$