A) \[\pi /6\]
B) \[\pi /2\]
C) \[3\pi /4\]
D) \[2\pi /3\]
Correct Answer: A
Solution :
Idea Equation of tangent of an ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] at\[\theta \]i.e., \[(a\cos \theta ,b\sin \theta )\]is\[\frac{x}{a}\cos \theta +\frac{y}{b}\cos \theta =1\]Now, compare the both equations of tangent to get \[\theta \]. Here, equation of tangent \[\frac{x}{a}\frac{\sqrt{3}}{2}+\frac{y}{b}\frac{1}{2}=1\] and equation of tangent at the point (a\[\cos \theta ,b\sin \theta \]) is\[\frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1\] Both are same i. e., \[\cos \theta +\frac{\sqrt{3}}{2},\sin \theta =\frac{1}{2}\Rightarrow \]\[\theta =\frac{\pi }{6}\] TEST Edge Equation of normal, latus rectum, based questions are asked. To solve these types of questions, students are advised to understand the concept of an ellipse.
You need to login to perform this action.
You will be redirected in
3 sec
