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Q)

Find the equation of the asymptotes to the hyperbola $36x^{2}-25y^{2}=900$

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A)
Toolbox:
  • (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:
$36x^2-25y^2=900$
The above equation is divided by $900$ we get,
$\large\frac{x^2}{25}-\frac{y^2}{36}$$=1$
$a^2=25,b^2=36$
$a=5,b=6$
Step 2:
$\large\frac{x}{a}$$\pm\large\frac{y}{b}$$=0$.
Substitute the value of a & b we get,
The equations of the asymptotes are $\large\frac{x}{5}$$\pm\large\frac{y}{6}$$=0$
(i.e) $6x\pm 5y=0$
This is the required equation of the asymptotes to the hyperbola.
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