SATHEE: Straight Line and Pair of Straight Lines 3 Question 13

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 $x + 5 y = λ$ . Since, area of triangle $= 5$

$\begin{aligned} \Rightarrow & \frac{1}{2} λ \cdot \frac{λ}{5} & = 5 \\ \Rightarrow & λ^{2} & = 50 \\ \Rightarrow & | λ | & = 5 \sqrt{2} \end{aligned}$

$∴$ Equation of the line $L$ is, $x + 5 y = \pm 5 \sqrt{2}$

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Straight Line and Pair of Straight Lines 3 Question 13

14. A straight line L is perpendicular to the line in 5x−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.

Solution:

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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 $L$ .