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The Catenary and Parabola are different curves that look similar; they are both "U" shaped and symmetrical, increasing infinitely on both sides to a minimum.
It has an absolute minimum at the point (2,3). It has no maximum but the ends of the graph both approach infinity.
maximum and minimum are both (-b/2a , c - (b^2/4a))
They both have an arc shape.
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).