Question

The eccentricity of the ellipse \[ \frac{(x - 1)^2}{2} + \left(y + \frac{3}{4}\right)^2 = \frac{1}{16} \] is: 

• A. \( \frac{1}{\sqrt{2}} \)
• B. \( \frac{1}{2\sqrt{2}} \)
• C. \( \frac{1}{2} \)
• D. \( \frac{1}{4} \)
• E. \( \frac{1}{4\sqrt{2}} \)

Hint:

Eccentricity is always between 0 and 1 for an ellipse. If your calculation yields something else, check if you swapped \( a^2 \) and \( b^2 \). The denominator of the smaller term always goes in the numerator of the fraction inside the root.

Answer 1

The Correct Option is A