Question

The equations of the lines which pass through the origin and are inclined at an angle $\tan ^ { - 1 } m$ to the line $y = m x + c$ are.

• A. $x = 0,2 m x + \left( m ^ { 2 } - 1 \right) y = 0$
• B. $y = 0,2 m x + \left( m ^ { 2 } - 1 \right) y = 0$
• C. $y = 0,2 m x + \left( 1 - m ^ { 2 } \right) y = 0$
• D. None of these

Answer 1

Answer: (B)

$y = 0,2 m x + \left( m ^ { 2 } - 1 \right) y = 0$

Answer 2

Angle between both the lines is

$\tan ^ { - 1 } m \pm \tan ^ { - 1 } m = \tan ^ { - 1 } \frac { 2 m } { 1 - m ^ { 2 } }$ or $\tan ^ { - 1 } 0$

Therefore equation of lines are $y = 0$ , $y = \frac { 2 m x } { 1 - m ^ { 2 } }$ .