Question

A line passing through the origin and making an angle $\frac{\pi }{4}$ with the line $y-3x=5$ has the equation

• A. $x+2y=0$
• B. $2x=y$
• C. $x=2y$
• D. $y+2x=0$

Answer 1

Answer: (C), (D)

$x=2y$
$y+2x=0$

Given equation of line $y=3x+5$

Hence $tan\theta =3$

$tan\alpha =tan\left(\frac{\pi }{4}\right)$

$=1$ $=|\frac{m_1-m_2}{1+m_1{m}_2}|$

Therefore, $\pm 1=\frac{m-3}{1+3m}$

Hence

$1+3m=m-3$
$2m=-4$

$m=-2$ ...(i) and

$m-3=-1-3m$

$4m=2$

$m=\frac{1}{2}$ ...(ii)

Therefore the equations of the lines are

$y=-2x$ and $y=\frac{x}{2}$

Hence, $2y=x$ and $2x+y=0$