Pair Of Straight Lines Question 131
If the lines $ ax^{2}+2hxy+by^{2}=0 $ represent the adjacent sides of a parallelogram, then the equation of second diagonal if one is $ lx+my=1 $ , will be
Options:
A) $ (am+hl)x=(bl+hm)y $
B) $ (am-hl)x=(bl-hm)y $
C) $ (am-hl)x=(bl+hm)y $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let the equation of lines represented by $ ax^{2}+2hxy+by^{2}=0 $ be $ y-m_1x=0 $ and $ y-m_2x=0 $ and one diagonal AC be $ lx+my=1. $
Therefore $ m_1+m_2=\frac{-2h}{b} $ and $ m_1m_2=\frac{a}{b} $
Now on solving the equation of OA and OC with the line AC, we get the coordinates of $ A( \frac{1}{l+mm_1},\frac{m_1}{l+mm_1} ) $ and $ C( \frac{1}{l+mm_2},\frac{m_2}{l+mm_2} ) $
Now find the coordinates of mid-point of AC and the equation of diagonal through this mid-point and origin.
The required equation is $ x(am-hl)=(lb-mh)y $ .
BETA
