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Briefly explain the focus and directrix of a parabola?

the set of points equidistant from a fixed point


What is a point that is equidistant from all points on 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.)


What is the locus of points in a plane that are equidistant from two fixed points?

I believe that is the definition of a straight line.


A perfectly round shape with all points equidistant from a fixed point or center is what?

a sphere


What is a three-dimensional surface in which all points are equidistant from a fixed point?

A 'spherical' surface.


What 3-dimensional figure is made from a set of points in space that are equidistant from a fixed point?

A sphere.


What geometric figure is described as the set of points equidistant from a fixed point?

It could be a circle or a sphere


Is the set of all points in a plane that are equidistant from a fixed point of the plane called the center?

That set of points forms what is known as a "circle".


The center of a circle is a example of what?

The center of a circle is an example of a point equidistant from all points on the circle's circumference, serving as the geometric midpoint of the shape. It is a key element for defining the circle's properties and relationships with other geometric figures.


A example of how a sphere is similar to a circle?

A circle, rotated about any diameter, will generate a sphere with the same radius. A circle is the locus of all points in 2-dimensional space that are equidistant from a fixed point. A sphere is the locus of all points in 3-dimensional space that are equidistant from a fixed point.


What figure is the locus of all points that are equidistant from two fixed points?

A line in 2D and a plane in 3D A perpendicular bisector of the line connecting the 2 given points


A compass draws all points that are equidistant from a fixed point thereby creating a locus of points for a circle?

A circle is the locus of all points equidistant from a given point, which is the center of the circle, and a circle can be drawn with a compass. (The phrase "locus of points for a circle" does not seem to be conventionally defined.) or true