Ellipses

"Consider two fixed lines in a Euclidean plane and a moving line, say a ruler, with two points marked on it. As the ruler moves subject to the condition that each of the marked points remains on one of the fixed lines, all other points on the ruler describe an ellipse." Berger and Gostiaux, Differential Geometry, p. 357.

Let the lines be the y and x axes and the points be (0, 1) and (1,0). The ruler has length two.

"Now consider the analogous problem in space: given three fixed planes, pairwise orthogonal for simplicity, and a moving line with three points marked, move the line around so that each of the marked points always lies on the same plane. As the line takes all possible positions, every point in it described an ellipsoid", Berger and Gostiaux, Differential Geometry, p. 357.