Q: What is the locus of all points that are a fixed distance from a given point?

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The locus of points at a given distance to a line would be a line parallel to the first line. Assuming that both lines are straight.

That's a sphere whose radius is the constant equal distance.

are the same distance from two points... Apex - TF

A pair of parallel lines at a distance of 1 cm from the line Q.

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A circle

line

It is the locus of points such that the sum of their distance from two distinct fixed points is a constant.

Straight line

It is the locus of all points such that their distance from a fixed line (the directrix) is the same as their distance from a fixed point which is not on that line (the focus).

true

A locus of points is just the set of points satisfying a given condition. The locus of points equidistant from a point is a circle, since a circle is just a set of points which are all the same distance away from the center

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 point. In fact it is fixed point and the locus of all points, in a plane that is a fixed distance from that fixed point defines the circle.

The locus of points at a given distance to a line would be a line parallel to the first line. Assuming that both lines are straight.

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