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 $\mathrm{L}{1}$ and $\mathrm{L}{2}$ passing through the origin. The tangent of an angle between the lines $\mathrm{L}{1}$ and $\mathrm{L}{2}$ 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 $\mathrm{A}=\left(\frac{5}{3}, \frac{8}{3}\right)$
Co-ordinates of $\mathrm{B}=\left(\frac{10}{3}, \frac{4}{3}\right)$
Slope of $\mathrm{OA}=\mathrm{m}_{1}=\frac{8}{5}$
Slope of $\mathrm{OB}=\mathrm{m}_{2}=\frac{2}{5}$
$\tan \theta=\left|\frac{m_{1}-m_{2}}{1+m_{1} m_{2}}\right|$
$\tan \theta=\frac{\frac{6}{5}}{1+\frac{16}{25}}=\frac{30}{41}$
$\tan \theta=\frac{30}{41}$
