Question

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 $5$. The equation of the line $L$ can be

• A. $x+5y+5\sqrt{2}=0$
• B. $x-5y+5\sqrt{2}=0$
• C. $x+5y-5\sqrt{2}=0$
• D. $x-5y-5\sqrt{2}=0$

Answer 1

Answer: (A), (C)

The correct options are
A $x+5y+5\sqrt{2}=0$
C $x+5y-5\sqrt{2}=0$

Slope of the line L is $5$.

The slope of the line perpendicular to the line L is $\frac{-1}{5}$ .

The equation of the line perpendicular to line L is $x+5y=c$, where $c$ is some constant.

Area of the triangle formed by this line with the axis is $\frac{c^2}{10}$.
$\Rightarrow \frac{c^2}{10}=5$
$\Rightarrow c=\pm 5\sqrt{2}$
The equation of the line L can be $x+5y=\pm 5\sqrt{2}.$