Let the eccentricity of an ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \), \( a > b \), be \( \frac{1}{4} \). If this ellipse passes through the point \( \left(-4\sqrt{\frac{2}{5}},\, 3\right) \), then \( a^2 + b^2 \) is equal to:
\( 29 \)
\( 31 \)
\( 32 \)
\( 34 \)
