Applications Of Derivatives Question 409
Question: Area of the greatest rectangle that can be inscribed in the ellipse $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $ is
[AIEEE 2005]
Options:
A) $ \sqrt{ab} $
B) $ \frac{a}{b} $
C) $ 2ab $
D) $ ab $
Show Answer
Answer:
Correct Answer: C
Solution:
Area of rectangle ABCD = $ (2a\cos \theta ) $ . $ (2b\sin \theta )=2ab\sin 2\theta $
Hence, area of greatest rectangle is equal to $ 2ab $ , when $ \sin 2\theta =1 $ .
BETA
