Question

Find the ecentricity and equation of the asympotes of the hyperbola 4x^2-9y^2=9

Answer 1

Given ,

$$4x^2-9y^2=9\\\implies \frac{x^2}{(\frac{3}{2})^2}-\frac{y^2}{1^2}=1$$

Thus, $a=\frac{3}{2},b=1$ and since, eccentricity is

$$e=\sqrt{1+(\frac{b}{a})^2}\\ \implies e=\frac{\sqrt{13}}{3}$$

Asymptotes of hyperbola is given by

$$\frac{x^2}{(\frac{3}{2})^2}-\frac{y^2}{1^2}=0\implies y=\pm\frac{2}{3}x$$