A plane curve proposed by Descartes to challenge Fermat's extremum-finding techniques. In parametric form, (1) (2) The curve has a discontinuity at . The left wing is generated as runs from to 0, the loop as ...
The conchoid of de Sluze is the cubic curve first constructed by René de Sluze in 1662. It is given by the implicit equation (1) or the polar equation (2) This can be written in parametric form as ...
A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of Geminus about 100 years later. Fermat and Roberval...
A cubic curve is an Algebraic curve of curve order 3. An Algebraic curve over a field is an equation , where is a polynomial in and with coefficients in , and the degree of is the maximum degree of each of its terms...
An ellipse is a curve that is the locus of all points in the plane the sum of whose distances and from two fixed points and (the foci) separated by a distance of is a given positive constant (Hilbert and Cohn-Vossen 1999,...
A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line (the conic section directrix) and a given point not on the line (the focus). The focal parameter (i.e.,...
A hyperbola (plural "hyperbolas"; Gray 1997, p. 45) is a conic section defined as the locus of all points in the plane the difference of whose distances and from two fixed points (the foci and ) separated by a distance ...
A circle is the set of points in a plane that are equidistant from a given point . The distance from the center is called the radius, and the point is called the center. Twice the radius is known as the diameter . The angle a...
The general bivariate quadratic curve can be written (1) Define the following quantities: (2) (3) (4) (5) Then the quadratics are classified into the types summarized in the following...
