Question

The eccentricity of the conic$9x^2-16y^2=144$ is

• A. $\frac{5}{4}$
• B. $\frac{4}{3}$
• C. $\frac{4}{5}$
• D. $\sqrt{7}$

Answer 1

The correct option is A

$\frac{5}{4}$

$Standardformofahyperbola$

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

$Here,a^2=16and{y}^2=9$

$\text{The eccentricity is calculated in the following way:}$

$b^2=a^2(e^2-1)$

$\Rightarrow 9=16(e^2-1)$

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

$\Rightarrow e^2=\frac{25}{16}$

$\Rightarrow e=\frac{5}{4}$