Pair Of Straight Lines Question 100
Question: If the slope of one of the line represented by the equation $ ax^{2}+2hxy+by^{2}=0 $ be l times that of the other, then
Options:
A) $ 4\lambda h=ab(1+\lambda ) $
B) $ \lambda h=ab{{(1+\lambda )}^{2}} $
C) $ 4\lambda h^{2}=ab{{(1+\lambda )}^{2}} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
It is given that $ m_2=\lambda m_1\Rightarrow m_1+\lambda m_1=\frac{-2h}{b} $
$ \Rightarrow m_1=\frac{-2h}{b(1+\lambda )} $ …..(i) and $ m_1.\lambda m_1=\frac{a}{b}\Rightarrow m_1=\sqrt{\frac{a}{b\lambda }} $ …(ii)
Hence, by (i) and (ii), $ \sqrt{\frac{a}{b\lambda }}=\frac{-2h}{b(1+\lambda )} $
On squaring both sides, we get $ 4\lambda h^{2}=ab{{(1+\lambda )}^{2}} $ .
BETA
