Consider an elliptic disc having uniform distribution of mass M as shown in figure. The moment of inertia (M.I.) about the major and minor
axis are $\frac{1}{4}{\mathrm{mb}}^2\text{ and }\frac{1}{4}{\mathrm{ma}}^2$respectively. Then

The M.I. about a line perpendicular to the plane of elliptic disc and passing through the centre O is $\frac{1}{4}\mathrm{M}\left({\mathrm{a}}^2+{\mathrm{b}}^2\right)$

The M.I. about a line, in its plane, passing through its centre and inclined at an angle $\mathrm{\theta }$ to the major axis is  $\frac{1}{4}\mathrm{m}\left({\mathrm{b}}^2{\cos }^2\mathrm{\theta }+{\mathrm{a}}^2{\sin }^2\mathrm{\theta }\right)$

The M.I. about a line, in its plane, passing through its centre and inclined at an angle $\mathrm{\theta }$ to the minor axis is $\frac{1}{4}\mathrm{m}\left({\mathrm{b}}^2{\sin }^2\mathrm{\theta }+{\mathrm{a}}^2{\cos }^2\mathrm{\theta }\right)$

The M.I. about a chord of length 2r passing through O and lying in plane of elliptic disc is $\frac{1}{4}\frac{{\mathrm{Ma}}^2{\mathrm{b}}^2}{{\mathrm{r}}^2}$