The set of all points collinear to two points is a?
By definition, the word "collinear" means that the points lie in
a LINE. The precise manner of line you are talking about
depends upon the geometric frame of reference you are using. For
example, in Euclidean geometry a line defined by two points is
usually taken to be "straight" like the intersection of two planes;
but in Global geometry such as the reality of the Earth's surface,
a line defined by two points is curved. If you fly from New York to
Tokyo, your line of flight is nearly a semicircle; we do not have
the technology to travel "straight" from New York to Tokyo through
the Earth's core.