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Q: The set of all points in a plane that are the same distance from a given point?

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In 2-dimensional space, a circle. In 3-dimensional space, a sphere.

Yes. That is obvious from the definition of a circle (or one possible definition): the set of all points in a plane that are at the same distance from a given point (the center of the circle).

It is the locus of a point such that the sum of its distance from two (distinct) fixed points is a constant. So, given two fixed points, F1 and F2, an ellipse is the locus of the point P such that PF1 + PF2 is a constant. That would be an ellipsoid, a 3 dimensional thing. The 2 distances have to be measured in a fixed (2 dimensional) plane.

A circle is the set of all the points that have the same distance from a given point (its center). If you rotate a shape, you rotate it in such a way that you keep any point a fixed distance from the center of rotation.

Any three points will determine a plane, provided they are not collinear. If you pick any two points, you can draw a line to connect them. An infinite number of planes can be drawn that include the line. But if you pick a third point that does not lie on the line. There will be exactly one plane that will contain the line and that point you added last. Only oneplane can contain the line, which was determined by the first two points, and the last point.

Related questions

a circle

A circle is the set of all points in a plane at a given distance FROM a given point, which is known as the circle's center.

They are points on the circumference of a unique circle in the plane.

A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the center.simplified, it is all the points on a plane that are the same distance from a given point.

true

CIRCLE

That's a "circle". The given distance is the circle's radius, and the given point is the circle's center.

These point are usually called loci as they are defined by a give set of rules.

circle

That is a circle.

That's a figure called a "circle". The given distance is the circle's radius, and the point is its center.

circle

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