It is a circle or a sphere that fits the given description
The answer is a circle or a sphere (or their equivalents in space with higher dimensions).
A circle
The centre of a circle is equal distance from all points of its circumference
8,070.000
Locus
parabola
circle
A sphere
It is the locus of all points such that their distance from a fixed line (the directrix) is the same as their distance from a fixed point which is not on that line (the focus).
The question is ambiguous. Is the"single" point fixed or floating?
A circle.
It is a graph of all points which are are the same distance (the radius) from a fixed point (the centre).
A circle is the set of all points in two dimensional space that are at the same distance from some fixed point.
Sphere
sounds like a sphere to me.
A solid sphere perhaps?
Alternates are fill-in-the-blank version of this Q. are the same distance from a point and a line
A globular sphere has all points at the same distance from an interiocenter point.