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- A circle can be defined as the locus of all points that are a certain distance from a given center.
- If we have a line and a point , a parabola is the locus of all points such that the distance from to .
- If we have two points A and B, an ellipse is the locus of all points such that is equal to a given constant.
- Given two points and and a constant , the locus of all points that satisfy is a circle (sometimes called an Apollonius circle).