Question

$\text{write the eccentricity of hyperbola}$

$9x^2-16y^2=144$

Answer 1

$We,have,$

$9x^2-16y^2=144$

$\Rightarrow \frac{9x^2}{144}-\frac{16y^2}{144}=1$

$\Rightarrow \frac{x^2}{16}-\frac{y^2}{9}=1$

$Itisoftheform\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,where{a}^2=16and{b}^2=9$

(Now,\)

$e=\sqrt{1+\frac{b^2}{a^2}}$

$=\sqrt{1+\frac{9}{16}}$

$=\sqrt{\frac{25}{16}}$

$=\frac{5}{4}$

$Hence,e==\frac{5}{4}$