What is the set of all points in a plane that are at a fixed distance from fixed point in a plane?

So, just a few points start to look like a circle, but when we collect ALL the points we will actually have a circle.

Try drawing one yourself (move any point):

images/geom-locus.js

(Note: the points are drawn as dots so you can see them,
but they really should have no size at all)

Surface

Imagine this happening in 3D space: all the points that are a fixed distance from a center make a sphere!

Locus

The idea of "the set of all points that ..." is used so much it has a name: Locus.

A Locus is a set of points that share a property.

So, a circle is "the locus of points on a plane that are a fixed distance from the center".

Note: "Locus" usually means that the points make a continuous curve or surface.

Example: An ellipse is the locus of points whose distance from two fixed points add up to a constant.

So, no matter where we are on the ellipse, we can add up the distance to point "F" and to point "G" and it will always be the same result.

What is a set of all points in plane that are at a fixed distance from a point called center?

What is the set of all points in a plane that are equidistant from a fixed line called and a fixed point not on the line?

Is the set of all points whose distance from a fixed point?

What do you call to the set of all points in a plane?