Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

Find the angle between the asymptotes of hyperbola $9(x-2)^{2}-4(y+3)^{2}=36$

Can you answer this question?

1 Answer

0 votes
  • (i) The asymptotes of $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$ are $\large\frac{x}{a}$$\pm\large\frac{y}{b}$$=0$.
  • (ii) They pass through the centre of the hyperbola.
  • (iii) Their slopes are $\large\frac{b}{a}$ and $-\large\frac{b}{a}$( i.e)the axes of the hyperbola bisect the angles between them.
  • (iv) The angle between the asymptotes $2\alpha=2\tan^{-1}\large\frac{b}{a}$$=2\sec^{-1}e$
Step 1:
The above equation is divided by $36$ we get
The hyperbola has its centre at $(2,-3)$ and $a^2=4,b^2=9$
$\Rightarrow a=2,b=3$
Step 2:
Let $2\alpha$ be the angle between the asymptotes.
$\Rightarrow 2\tan^{-1}\large\frac{3}{2}$
The angle between the asymptotes is $2\tan^{-1}\large\frac{3}{2}$
answered Jun 24, 2013 by sreemathi.v

Related questions

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