First slide

Equation of line in Straight lines

Question

The slope of a line is $3$ times the slope of the other line and the tangent of the angle between them is $4 / 13$ , sum of their slopes is equal to

Moderate

A

2
B

4
C

6
D

8

Solution

Let the slopes of the given lines be $m$ and $3$ m. if $θ$ is the angle between them then
$\begin{array}{l} \tan θ = \frac{| 3 m - m |}{1 + (3 m) (m)} = \frac{4}{13} \\ \Rightarrow \pm 2 m \times 13 = 4 (1 + 3 m^{2}) \\ \Rightarrow 6 m^{2} \pm 13 m + 2 = 0 \end{array}$
$\Rightarrow m = \frac{1}{6}$ or $2$ and $m = - \frac{1}{6}$ or $- 2 .$
For $m = 2,$ the sum of the slopes is $4 m = 8$

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