parabola
A parabola.
A Circle.
A line.
If your asking "What is ...?" Then, the answer is a circle. This is the definition of a circle!
The set of all points in a plane that are equidistant from a single point and a single line
The set of all points in the plane equidistant from one point in the plane is named a parabola.
parabola
A parabola.
It is a parabola.
A Circle.
Math
circle
a circle, centered at the given point.
That set of points forms what is known as a "circle".
The center of the circle. That's how the circle is defined. (The collection of all points on a plane equidistant from a fixed point. The fixed point is the center and the fixed distance is the radius.)
In spherical geometry we look at the globe as the sphere S^2. Any plane intersecting the sphere will create a great circle. Now if you take any point on the globe and reflect it across that plane, you have another point that is equidistant from the plane. The sets of all these points will be equidistant from the great circle.