Straight Line and Pair of Straight Lines 3 Question 13
14. $A$ straight line $L$ is perpendicular to the line in $5 x-y=1$. The area of the triangle formed by the line $L$ and the coordinate axes is 5 . Find the equation of the line $L$.
(1980, 3M)
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Solution:
- A straight line perpendicular to $5 x-y=1$ is $x+5 y=\lambda$. Since, area of triangle $=5$
$$ \begin{array}{rlrl} \Rightarrow & & \frac{1}{2} \lambda \cdot \frac{\lambda}{5} & =5 \\ \Rightarrow & \lambda^{2} & =50 \\ \Rightarrow & |\lambda| & =5 \sqrt{2} \end{array} $$
$\therefore \quad$ Equation of the line $L$ is, $x+5 y= \pm 5 \sqrt{2}$
