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

• (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$
$36x^2-25y^2=900$
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) $6x\pm 5y=0$