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

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

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

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

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