Straight Lines Question 2
Question 2 - 2024 (27 Jan Shift 1)
The portion of the line $4 x+5 y=20$ in the first quadrant is trisected by the lines $L _1$ and $L _2$ passing through the origin. The tangent of an angle between the lines $L _1$ and $L _2$ is :
(1) $\frac{8}{5}$
(2) $\frac{25}{41}$
(3) $\frac{2}{5}$
(4) $\frac{30}{41}$
Show Answer
Answer (4)
Solution
Co-ordinates of $A=\left(\frac{5}{3}, \frac{8}{3}\right)$
Co-ordinates of $B=\left(\frac{10}{3}, \frac{4}{3}\right)$
Slope of $OA=m _1=\frac{8}{5}$
Slope of $OB=m _2=\frac{2}{5}$
$\tan \theta=\left|\frac{m _1-m _2}{1+m _1 m _2}\right|$
$\tan \theta=\frac{\frac{6}{5}}{1+\frac{16}{25}}=\frac{30}{41}$
$\tan \theta=\frac{30}{41}$
