line
Straight line
parabola
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.
A circle
This is the definition of a circle.
Straight line
The locus of all points that are the same distance from two given points is a perpendicular bisector of the line segment connecting those two points. This line is equidistant from each of the two points at all locations along its length.
A locus of points is just the set of points satisfying a given condition. The locus of points equidistant from a point is a circle, since a circle is just a set of points which are all the same distance away from the center
are the same distance from two points... Apex - TF
parabola
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.
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 center isn't the locus, and a point on the circumference isn't the locus.The whole circumference of the circle is the locus.It's the locus of all points that have the same distance from the center of the circle.
It can allow you to define shapes but that is not quite the same thing as an object.
A circle
The locus of points where the potential due to an isolated point charge is constant is a spherical surface centered on the point charge. This is because the potential decreases with distance from the point charge, so points at the same distance will have the same potential.
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.