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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.

Q: Which geometric object is defined as the set if all points in a plane at a given distance at a given point?

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parabola

False, other geometric objects exist which can be defined as a parrticular locus of points, such as the parabola and the hyperbola.

Points are the only such objects.

Strictly speaking, the only geometric item that has neither length nor width is a "point", but as such, it is not considered a "figure". A geometric figure is defined as a "set of points". I suppose a point could be thought of as a set containing only one element, but that rather contradicts the intention of the definition where it refers to points in the plural.As Euclid defined it: A figure is that which is contained by any boundary or boundaries.

Yes, because the distance is a metric which is defined in that way.

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Circle

circle

The metric of a geometric space is defined as the distance between two points.

imagine it ... a circle

The universe.

line

parabola

Parabola - apex

The bisector of that angle.

They are parallel lines

Parallel lines could fit the given criterior

parabola