Straight Line Question 391

Question: The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is ? 1 is [AIEEE 2004]

Options:

A) $ \frac{x}{2}-\frac{y}{3}=1 $ and $ \frac{x}{-2}+\frac{y}{1}=1 $

B) $ \frac{x}{2}-\frac{y}{3}=-1 $ and $ \frac{x}{-2}+\frac{y}{1}=-1 $

C) $ \frac{x}{2}-\frac{y}{3}=1 $ and $ \frac{x}{2}+\frac{y}{1}=1 $

D) $ \frac{\pi }{3} $ and $ \frac{x}{-2}+\frac{y}{1}=-1 $

Show Answer

Answer:

Correct Answer: A

Solution:

  • Here $ a+b=-1 $ . Required line is $ \frac{x}{a}-\frac{y}{1+a}=1 $ …..(i)Since line (i) passes through (4, 3) $ \therefore $ $ \frac{4}{a}-\frac{3}{1+a}=1 $

$ \Rightarrow $ $ 4+4a-3a=a+a^{2} $
Þ $ a^{2}=4\Rightarrow a=\pm 2 $

$ \therefore $ Required lines are $ \frac{x}{2}-\frac{y}{3}=1 $ and $ \frac{x}{-2}+\frac{y}{1}=1 $ .