Pair Of Straight Lines Question 136
Question: If the lines represented by the equation $ 2x^{2}-3xy+y^{2}=0 $ make angles $ \alpha $ and $ \beta $ with x-axis, then $ {{\cot }^{2}}\alpha +{{\cot }^{2}}\beta $ =
Options:
A) 0
B) 3/2
C) 7/4
D) 5/4
Show Answer
Answer:
Correct Answer: D
Solution:
$ m_1=\tan \alpha $ and $ m_2=\tan \beta $
$ \Rightarrow \cot \alpha =\frac{1}{m_1} $ and $ \cot \beta =\frac{1}{m_2} $
Hence, $ {{\cot }^{2}}\alpha +{{\cot }^{2}}\beta =\frac{1}{m_1^{2}}+\frac{1}{m_2^{2}}=\frac{m_1^{2}+m_2^{2}}{{{(m_1m_2)}^{2}}} $
$ =\frac{{{(m_1+m_2)}^{2}}-2m_1m_2}{{{(m_1m_2)}^{2}}}=\frac{{{(3)}^{2}}-2(2)}{{{(2)}^{2}}}=\frac{5}{4} $ .
BETA
