line
Straight line
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.
parabola
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
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.
parabola
The locus of points that are the same distance from a point and a line is a parabola. In this scenario, the point acts as the focus of the parabola, while the line serves as the directrix. The shape of the parabola opens away from the line, with all points on the curve equidistant from both the focus and the directrix.
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 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).
It can allow you to define shapes but that is not quite the same thing as an object.
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.
A circle