Straight Line Question 133
Question: Let L be the line $ 2x+y=2 $ . If the axes are rotated by $ 45^{o} $ , then the intercepts made by the line L on the new axes are respectively [Roorkee Qualifying 1998]
Options:
A) $ \sqrt{2} $ and 1
B)1 and $ \sqrt{2} $
C) $ 2\sqrt{2} $ and $ 2\sqrt{2}/3 $
D) $ 2\sqrt{2}/3 $ and $ 2\sqrt{2} $
Correct Answer: C $ \Rightarrow \frac{1}{p}=\frac{1}{\sqrt{2}}+\frac{1}{2}.\frac{1}{\sqrt{2}}=\frac{3}{2\sqrt{2}} $ \ $ p=\frac{2\sqrt{2}}{3} $ ; \ $ \frac{1}{q}=-\frac{1}{1}\sin 45^{o}+\frac{1}{2}\cos 45^{o} $ $ \frac{1}{q}=\frac{-1}{\sqrt{2}}+\frac{1}{2\sqrt{2}}=-\frac{1}{2\sqrt{2}},\therefore q=2\sqrt{2} $ So intercept made by is assume on the new axis $ ( 2\sqrt{2}/3,2\sqrt{2} ) $ . If the rotation is assume in clockwise direction, so intercept made by the line on the new axes would be $ ( 2\sqrt{2},2\sqrt{2}/3 ) $ .Show Answer
Answer:
Solution:
Þ $ \frac{1}{p}=\frac{1}{a}\cos \alpha +\frac{1}{b}\sin \alpha \Rightarrow \frac{1}{q}=-\frac{1}{a}\sin \alpha +\frac{1}{b}\cos \alpha $
Þ $ \frac{1}{p}=\frac{1}{1}\cos 45^{o}+\frac{1}{2}\sin 45^{o} $
BETA
