Hausdorff distance can be used in various areas, where the problems of shape matching and comparison appear. We look at the Hausdorff distance between two hyperspheres in $\mathbb{R}^n$. With respect to different geometric objects, the Hausdorff distance between a segment and a hypersphere in $\mathbb{R}^n$ is given, too. Using the Mahalanobis distance, a modified Hausdorff distance between a segment and an ellipse in the plane, and generally between a segment and a hyper-ellipsoid in $\mathbb{R}^n$ is adopted. Finally, the modified Hausdorff distance between ellipses is obtained.