Question: The equation of the line which makes right angled triangle with axes whose area is 6 sq. units and whose hypotenuse is of 5 units, is
Options:
A) $ \frac{x}{4}+\frac{y}{3}=\pm \ 1 $
B) $ \frac{x}{4}-\frac{y}{3}=\pm \ 3 $
C) $ \frac{x}{6}+\frac{y}{1}=\pm \ 1 $
D) $ \frac{x}{1}-\frac{y}{6}=\pm \ 1 $
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Answer:
Correct Answer: A
Solution:
- If the line is $ \frac{x}{a}+\frac{y}{b}=1 $ , then the intercepts on the axes are $ a $ and $ b $ . Therefore the area is $ \frac{1}{2}|a\times b|=6\Rightarrow |ab|=12 $ ?..(i) and hypotenuse is 5, therefore $ a^{2}+b^{2}=25 $ ?..(ii) On solving (i) and (ii), we get $ a=\pm 4 $ or $ \pm 3 $ and $ b=\pm 3 $ or $ \pm 4 $ Hence equation of line is $ \pm \frac{x}{4}\pm \frac{y}{3}=1 $ or $ \pm \frac{x}{3}\pm \frac{y}{4}=1 $ .Trick: Check with options. Obviously, the line $ \frac{x}{4}+\frac{y}{3}=\pm 1 $ satisfies both the conditions.
BETA
