SATHEE: Straight Line Question 6

Straight Line Question 6

Question: If the lines $ y=3x+1 $ and $ 2y=x+3 $ are equally inclined to the line $ y=mx+4, $ then m = [ISM Dhanbad 1976]

Options:

A) $ \frac{1+3\sqrt{2}}{7} $

B) $ \frac{1-3\sqrt{2}}{7} $

C) $ \frac{1\pm 3\sqrt{2}}{7} $

D) $ \frac{1\pm 5\sqrt{2}}{7} $

Show Answer

Answer:

Correct Answer: D

Solution:

$ m_1=3,m_2=\frac{1}{2} $ and $ m_3=m $ Let the angle between first and third line is $ {\theta_1} $ and between second and third is $ {\theta_2} $ , then $ \tan {\theta_1}=\frac{3-m}{1+3m} $ and $ \tan {\theta_2}=\frac{m-\frac{1}{2}}{1+\frac{m}{2}} $ But $ {\theta_1}={\theta_2}\Rightarrow \frac{3-m}{1+3m}=\frac{m-\frac{1}{2}}{1+\frac{m}{2}} $
Þ $ 7m^{2}-2m-7=0 $ Þ $ m=\frac{1\pm 5\sqrt{2}}{7} $ .

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Straight Line Question 6

Question: If the lines $ y=3x+1 $ and $ 2y=x+3 $ are equally inclined to the line $ y=mx+4, $ then m = [ISM Dhanbad 1976]

Options:

Answer:

Solution:

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