Straight Line Question 274

Question: If the lines $ y=(2+\sqrt{3})x+4 $ and $ y=kx+6 $ are inclined at an angle $ 60{}^\circ $ to each other, then the value of k will be

Options:

A) 1

B) 2

C) -1

D) -2

Show Answer

Answer:

Correct Answer: C

Solution:

  • [c] $ y=(2+\sqrt{3})x+4 $ ? (1) $ y=k\alpha +6 $ ? (2) By (1)
    $ \Rightarrow m_1=(2+\sqrt{3}); $ by (2)
    $ \Rightarrow m_2=k $

$ \therefore \tan 60{}^\circ =\frac{m_1-m_2}{1+m_1m_2}\Rightarrow k=-1 $