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Earn +20 ptsQ: Infinite number of points equidistant from a given point?
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The set of all points in a plane equidistant from a given point?
a circle, centered at the given point.
The locus of all points in space equidistant from a given point?
That's a sphere whose radius is the constant equal distance.
What is the greatest number of planes that can pass through three collinear points?
The points are collinear, and there is an infinite number of planes that contain a given line. A plane containing the line can be rotated about the line by any number of degrees to form an unlimited number of other planes.If, on the other hand, the points are not collinear, then the plane has no wriggle room: it is stuck fast in one place - there can be only one plane containing all the points. Provided they are non-colinear, three points will define a plane.
What is a plane curve that is everywhere equidistant from a given fixed point its center?
A circle.
Does every line have an infinite number of lines parallel to the given line?
Yes it's quite possible if need be.
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