Straight Line Question 398
Question: The line parallel to the x-axis and passing through the intersection of the lines $ ax+2by+3b=0 $ and $ bx-2ay-3a=0 $ , where $ (a,b)\ne (0,0) $ is [AIEEE 2005]
Options:
A)Above the x-axis at a distance of 3/2 from it
B)Above the x-axis at a distance of 2/3 from it
C)Below the x-axis at a distance of 3/2 from it
D)Below the x-axis at a distance of 2/3 from it
Correct Answer: C $ \Rightarrow (a+b\lambda )x $ $ +(2b-2a\lambda )y+3b-3\lambda a=0 $ ?..(i) Line (i) is parallel to x-axis, Show Answer
Answer:
Solution:
$ \therefore $ $ a+b\lambda =0\Rightarrow \lambda =\frac{-a}{b}=0 $ Put the value of $ \lambda $ in (i) $ ax+2by+3b-\frac{a}{b}(bx-2ay-3a)=0 $ $ y( 2b+\frac{2a^{2}}{b} )+3b+\frac{3a^{2}}{b}=0 $ , $ y( \frac{2b^{2}+2a^{2}}{b} )=-( \frac{3b^{2}+3a^{2}}{b} ) $ $ y=\frac{-3(a^{2}+b^{2})}{2(b^{2}+a^{2})}=\frac{-3}{2} $ , $ y=-\frac{3}{2} $ So, it is 3/2 unit below x-axis.
BETA
