If they are in the same plane, then they share a common plane. Did you mean to say common point. If that's the case where they are in the same plane, but do not share a common point, then they are parallel lines.
circle
parallel
This is the definition of a circle.
"Circle". That "same distance" is the radius of the circle, and that "given point" is the center of the circle.
A circle. However, that DOES depend on the Euclidean metric being used for measuring distance.
Noncoplanar is a term in geometry referring two or more figures, lines, or points that do not all lie in the same plane.
I'm not sure if I fully understand your question, but I think the term you're looking for is coplanar.
it means that you are plotting the points on a graph, or XY coordinate plane
Cognates.
co-planar
Circle