Straight Line Question 383

Question: For what values of a and b the intercepts cut off on the coordinate axes by the line $ ax+by+8=0 $ are equal in length but opposite in signs to those cut off by the line $ 2x-3y+6=0 $ on the axes [MP PET 1983]

Options:

A) $ a=\frac{8}{3},\ b=-\ 4 $

B) $ a=-\frac{8}{3},\ b=-\ 4 $

C) $ a=\frac{8}{3},\ b=4 $

D) $ a=-\frac{8}{3},\ b=4 $

Show Answer

Answer:

Correct Answer: D

Solution:

  • The equation of lines in intercept form are $ \frac{x}{-8/a}+\frac{y}{-8/b}=1 $ …..(i) $ \frac{x}{-3}+\frac{y}{2}=1 $….. (ii) According to the condition, $ -\frac{8}{a}=-(-3) $

$ \Rightarrow a=-\frac{8}{3} $ and $ -\frac{8}{b}=-(2)\Rightarrow b=4 $ .