logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Coordinate Geometry
0 votes

If angle between the asymptotcs of the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$is $45^{\circ}$ then value of eccentricity $e$ is :

$\begin{array}{1 1}(A)\;\sqrt {4 \pm 2 \sqrt {2}} \\(B)\;\sqrt {4 + 2 \sqrt {2}} \\(C)\;\sqrt {4 - 2 \sqrt {2}} \\(D)\;none\;of\;these \end{array}$

Can you answer this question?
 
 

1 Answer

0 votes
$2 \tan^{-1} \large\frac{b}{a} $$=45^{\circ}$
=> $\large\frac{b}{a}$$=\tan 22 \large\frac{1}{2}$$ ^{\circ}$
$\qquad = \large\frac{a^2(e^2-1)}{a^2}$$(\sqrt 2-1)^2$
=> $e^2-1=3-2 \sqrt 2$
=> $e=\sqrt {4-2 \sqrt 2}$
Hence C is the correct answer.
answered Apr 21, 2014 by meena.p
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...