"Circle". That "same distance" is the radius of the circle,
and that "given point" is the center of the circle.
A circle
A circle. However, that DOES depend on the Euclidean metric being used for measuring distance.
A circle
A spherical surface, with its center at the given point, and its radius equal to the given distance.
They form the sphere whose center is the given point and whose radius is the given distance.
circle
Straight line
The set of all points in a plane at a given distance from a given point.clock
true
A circle
A circle. However, that DOES depend on the Euclidean metric being used for measuring distance.
A circle or a sphere would fit the given description.
A sphere is a solid bounded by the set of all points at a given distance from a given point.
Given a straight line (a directrix) and a point (the focus) which is not on that line, a parabola is locus of all points whose distance form the directrix is the same as its distance from the focus.
In three dimensions, the solid defined as being bound by the set of points at a given distance form a point is a sphere. In two dimensions, the figure defined as being bound by the set of points at a given distance from a point is a circle. In one dimension, a line segment is bound by the two points at a given distance from a point.
A circle
The set of all points a given distance from a center point is a circle. The given distance is the radius, and the given point is the center. Or, in 3 dimensional space, a sphere.