Conic Sections Question 335
Question: Tangent is drawn to ellipse $ \frac{x^{2}}{27}+y^{2}=1 $ at $ (3\sqrt{3}\cos \theta ,\ \sin \theta ) $ where $ \theta \in (0,\ \pi /2) $ . Then the value of $ \theta $ such that sum of intercepts on axes made by this tangent is minimum, is
[IIT Screening 2003]
Options:
A) $ \pi /3 $
B) $ \pi /6 $
C) $ \pi /8 $
D) $ \pi /4 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{x\cos \theta }{3\sqrt{3}}+y\sin \theta =1. $
Sum of intercepts = $ 3\sqrt{3} $
$ \sec \theta +cosec\theta =f(\theta ) $ , (say) $ f’(\theta )=\frac{3\sqrt{3}{{\sin }^{3}}\theta -{{\cos }^{3}}\theta }{{{\sin }^{2}}\theta {{\cos }^{2}}\theta } $ . At $ \theta =\frac{\pi }{6},f(\theta ) $ is minimum.
BETA
