Question

The eccentricity of the hyperbola $16x^2-9y^2=1$ is

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

Answer 1

Answer: (B)

$\frac{5}{3}$

Equation of hyperbola: $16x^2-9y^2=1$

can be written as $\frac{x^2}{\frac{1}{16}}+\frac{y^2}{\frac{1}{9}}=1$

$e^2=1+\frac{b^2}{a^2}=1+\frac{16}{9}=\frac{25}{9}$

or, $e=\frac{5}{3}$

Hence, B is the correct option.