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In its standard form, the equation of a circle is a quadratic in both variables, x and y, whereas a parabola is quadratic in one (x) and liner in the other (y).

A circle is a closed shape and comprises the locus of all points that are equidistant from one given point (the centre).

A parabola is an open shape and comprises the locus of all points that are the same distance from a a straight line (the directrix) and a point not on that line (the focus).

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