Circle.
One definition of a parabola is the set of points that are equidistant from a given line called the directrix and a given point called the focus. So, no. The distances are not different, they are the same. The distance between the directrix and a given point on the parabola will always be the same as the distance between that same point on the parabola and the focus. Any point where those two distances are equal would be on the parabola somewhere and all the points where those two distances are different would not be on the parabola. Note that the distance from a point to the directrix is definied as the perpendicular distance (also known as the minimum distance).
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.
That's a "circle". The given distance is the circle's radius, and the given point is the circle's center.
A sphere is a solid bounded by the set of all points at a given distance from a given point.
It is the circle's radius
That's a figure called a "circle". The given distance is the circle's radius, and the point is its center.
One definition of a parabola is the set of points that are equidistant from a given line called the directrix and a given point called the focus. So, no. The distances are not different, they are the same. The distance between the directrix and a given point on the parabola will always be the same as the distance between that same point on the parabola and the focus. Any point where those two distances are equal would be on the parabola somewhere and all the points where those two distances are different would not be on the parabola. Note that the distance from a point to the directrix is definied as the perpendicular distance (also known as the minimum distance).
It is called a circle.
circle, but the given end point is called the center of a circle : )
These point are usually called loci as they are defined by a give set of rules.
The set of all points in space that are the same distance from a given point is called a sphere.
It is a sphere.
A spherical surface, with its center at the given point, and its radius equal to the given distance.
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.
They form the sphere whose center is the given point and whose radius is the given distance.
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.
That's a "circle". The given distance is the circle's radius, and the given point is the circle's center.