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".
Circle
Circle
The set of all points in a plane that are equidistant from a single point and a single line
A parabola.
parabola
Yes, a parabola always has a vertex. However, it may not always have roots. The roots of a parabola are the x-values where the parabola intersects the x-axis. It is possible for a parabola to have two, one, or no roots depending on the discriminant of the quadratic equation.
A circle or a sphere would fit the given description.
The answer will depend on what the "certain distances" are for each point.
It is a parabola.