Question

$\text{The eccentricity of the hyperbola}{x}^2-4y^2=1is$

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{\sqrt{5}}{2}$
• C. $\frac{2}{\sqrt{3}}$
• D. $\frac{2}{\sqrt{5}}$

Answer 1

The correct option is B

$\frac{\sqrt{5}}{2}$

$\text{The equation of the hyperbola is}{x}^2-4y^2=1$

$\text{This can be reqritten in the following way :}$

$\frac{x^2}{1}-\frac{y^2}{1/4}=1$

$\text{This is the standard form of a hyperbola,}$

$Where{a}^2=1and{b}^2=\frac{1}{4}$

$\text{The value of eccentricity is calculated n the following way :}$

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

$\Rightarrow \frac{1}{4}=(e^2-1)$

$\Rightarrow e^2=\frac{5}{4}$

$\Rightarrow e=\frac{\sqrt{5}}{2}$