Straight Line Question 297

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

Options:

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

B) $ y=0,\ \ 2mx+(m^{2}-1)\ y=0 $

C) $ y=0,\ \ 2mx+(1-m^{2})\ y=0 $

D)None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  • Angle between both the lines is $ {{\tan }^{-1}}m\pm {{\tan }^{-1}}m={{\tan }^{-1}}\frac{2m}{1-m^{2}} $ or $ {{\tan }^{-1}}0 $ Therefore equation of lines are $ y=0 $ , $ y=\frac{2mx}{1-m^{2}} $ .