Quantitative Aptitude Ques 274
Question: If $ x=a\sin \theta -b\cos \theta , $ $ y=a\cos \theta +b\sin \theta , $ then which of the following is true?
Options:
A) $ x^{2}+y^{2}=a^{2}+b^{2} $
B) $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $
C) $ x^{2}+y^{2}=a^{2}-b^{2} $
D) $ \frac{x^{2}}{y^{2}}+\frac{a^{2}}{b^{2}}=1 $
Show Answer
Answer:
Correct Answer: A
Solution:
- We have, $ x=a\sin \theta -b\cos \theta $
$ \therefore $ $ x^{2}=a^{2}{{\sin }^{2}}\theta +b^{2}\cos \theta -2ab\sin \theta \cdot \cos \theta $ Similarly, $ y^{2}=a^{2}{{\cos }^{2}}\theta +b^{2}{{\sin }^{2}}\theta +2ab\sin \theta \cdot \cos \theta $
$ \therefore $ $ x^{2}+y^{2}=a^{2}+b^{2} $
BETA
