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Certainly false for parabolae; a parabola is the locus of points in a plane which are equidistant from a point (the focus) and a line (the directrix) in that plane. It's also false for an ellipse, which is the locus of points in a plane where the sum of the distances from two other points in that plane (the foci) is constant. AND false for a hyperbola, which is the locus of points in a plane where the absolute value of the DIFFERENCE in the distance from two points in that plane (also the foci) is constant. Alternatively, a hyperbola is the locus of points in a plane where the ratio of the distance to one of the foci and to a line (the directrix) is constant (which is larger than 1; if it's exactly equal to 1, you get a parabola instead).

All of these are only slightly more complicated than circles, and in fact they, alone with circles, are called "conic sections" because they all are formed by the intersection of a plane with a right circular conical surface.

Q: Although the locus of points idea can be used to define a straight line and circle more complex shapes such as parabolas must be defined a different way. True or False?

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