Question

The eccentricity of the hyperbola \( x^{2} - 4y^{2} = 1 \) is:

• A. $\frac{\sqrt{5}}{2}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{5}{4}$
• D. $\frac{3}{2}$

Hint:

Eccentricity of a hyperbola is always greater than 1.

Answer 1

The Correct Option is A

Step 1: Concept
Standard hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ has eccentricity $e = \sqrt{1 + \frac{b^2}{a^2}}$.
Step 2: Analysis
Given $x^{2} - \frac{y^{2}}{1/4} = 1$, so $a^{2} = 1$ and $b^{2} = 1/4$.
$e = \sqrt{1 + \frac{1/4}{1}} = \sqrt{5/4}$.
Step 3: Conclusion
$e = \frac{\sqrt{5}}{2}$.
Final Answer: (A)