= Solution
{c}
The <second moment of area> about an axis weights each element of <cross-sectional area> by its squared perpendicular distance from that axis. The <ellipse> extends farther along $\mathbf d_2$ than along $\mathbf d_1$, so its material lies, on balance, farther from the $\mathbf d_1$ axis. Therefore
$$
\boxed{I_1>I_2.}
$$
With zero <intrinsic curvature of an elastic filament>, the respective <bending moments> required by the <constitutive equation> are $EI_1\kappa\mathbf d_1$ and $EI_2\kappa\mathbf d_2$. Thus their magnitudes satisfy
$$
\boxed{|m_{\mathbf d_1}|=EI_1|\kappa|>EI_2|\kappa|=|m_{\mathbf d_2}|}
$$
for $\kappa\ne0$: bending about the minor axis is harder. Here $E$ is <Young's modulus>, and $EI_i$ is the corresponding <bending stiffness>.
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