Pair Of Straight Lines Question 8
Question: If the equation $ ax^{2}+2hxy+by^{2}=0 $ represents two lines $ y=m_1x $ and $ y=m_2x $ , then
[CEE 1993; MP PET 1988]
Options:
A) $ m_1+m_2=\frac{-2h}{b} $ and $ m_1m_2=\frac{a}{b} $
B) $ m_1+m_2=\frac{2h}{b} $ and $ m_1m_2=\frac{-a}{b} $
C) $ m_1+m_2=\frac{2h}{b} $ and $ m_1m_2=\frac{a}{b} $
D) $ m_1+m_2=\frac{2h}{b} $ and $ m_1m_2=-ab $
Show Answer
Answer:
Correct Answer: A
Solution:
The given equation represents two lines $y=m_1 x$ and $y=m_2$ x.
From the equation $ax^2 +2hxy+by^2 =0,$ we can infer that the sum of the slopes of the lines is equal to the negative ratio of thecoefficient of the $xy$-term to the coefficient of the $x^2$ term, and the product of the slopes of the lines is equal to the ratio of the constant term to the coefficient of the $x^2$ term.
Therefore, the correct answer is A) $m_1 m_1+m_2=\frac{-2h}{b} $ and $ m_1m_2=\frac{a}{b} $
BETA
