Question

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

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

Answer 1

Answer: (B)

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

Answer 2

A line perpendicular to the line $5 x - y = 1$is given by $x + 5 y - \lambda = 0 = L$ , (given)

In intercept form $\frac { x } { \lambda } + \frac { y } { \lambda / 5 } = 1$

So, area of triangle is $\frac { 1 } { 2 }$ $x$ (Multiplication of intercepts)

⇒ $\frac { 1 } { 2 } ( \lambda ) \times \left( \frac { \lambda } { 5 } \right) = 5 \Rightarrow \lambda = \pm 5 \sqrt { 2 }$

Hence the equation of required straight line is

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