Question

The eccentricity of the hyperbola \( \frac{\sqrt{1999}}{3} \left( x^2 - y^2 \right) = 1 \) is

• A. \( \sqrt{2} \)
• B. 2
• C. \( 2\sqrt{2} \)
• D. \( \sqrt{3} \)

Hint:

For hyperbolas, the eccentricity is always greater than 1, and it can be found by the formula \( e = \sqrt{1 + \frac{b^2}{a^2}} \).

Answer 1

The Correct Option is A

The general equation of a hyperbola is \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \). The eccentricity \( e \) of a hyperbola is given by: \[ e = \sqrt{1 + \frac{b^2}{a^2}} \] Comparing the given equation with the standard form, we find that the eccentricity is \( \sqrt{2} \).