Locus
Circle
A circle or a sphere would fit the given description.
It is a parabola.
It is the circle's radius
The apothem is the distance from the center to the middle of any side on a regular polygon. That is, a shape with every single side and angle the same.
A parabola has a single focus point. There is a line running perpendicular to the axis of symmetry of the parabola called the directrix. A line running from the focus to a point on the parabola is going to have the same distance as from the point on the parabola to the closest point of the directrix. In theory you could look at a parabola as being an ellipse with one focus at infinity, but that really doesn't help any. ■
A parabola is a single curve: it does not have separate parts.
===> "circle", with center at the "single point" and radius of the "certain distance".
The function that describes the force acting on a single atom as a function of the distance r is denoted as f(r) and is known as the interatomic potential energy function.
Circle
Circle
The set of all points in a plane that are equidistant from a single point and a single line
parabola
A parabola.
An x2 parabola will always have one vertex, but depending on the discriminant of the function (b2-4ac) the parabola will either have 2 roots (it crosses the x-axis twice), 1 repeating root (the parabola meets the x-axis at a single point), or no real roots (the parabola doesn't meet the x-axis at all)
A circle or a sphere would fit the given description.
The answer will depend on what the "certain distances" are for each point.