For line to be tangent to a given curve, they should pass through a common point and both should have same slope at that point. But how do we compare slope in 3D?
E.g.=> For a circle in 2-Dimensions, we know which lines will be it's tangents. But what if I ask, which lines will be tangent to it in 3-Dimensions? Will the answer be same for both cases, or will many others lines, lying in some other planes, also be included?
All I could think of is that, we need to find tangents in planes, and in every plane the curve will be set of points, except the one in which the curve is a circle. And because slope of a point is not defined, there will be no new tangents added when we go from 2D to 3D.