A line is the locus of points such that the gradient (slope) between that point and one fixed point in the plane is a constant.
Technically, that definition does not include a vertical line because its gradient is not defined! You could get around that this by requiring that either the gradient is a constant or, if it is undefined, then the inverse gradient (dx/dy) is constant.
a straight line ..
I believe that is the definition of a straight line.
The locus of all points that are the same distance from two given points is a perpendicular bisector of the line segment connecting those two points. This line is equidistant from each of the two points at all locations along its length.
Two parallel lines.
The perpendicular bisector of the line joining the two points.
No. A line is the locus of all points located between any two points.
a straight line ..
line
are the same distance from two points... Apex - TF
All points on the same line are colinear but if you mean what are the points all called collectively - they represent a "locus of points".
The locus of points at a given distance to a line would be a line parallel to the first line. Assuming that both lines are straight.
The perpendicular bisector of the straight line joining the two points.
parabola
I believe that is the definition of a straight line.
Straight line
A line that is the angle bisector.
Two parallel lines.