The quartic curve with implicit equation (1) It has crunodes at , , and . The horizontal asymptotes are at , , and . The vertical asymptotes are at and The polar equation is given by solving the quadratic equation ...
A general plane quartic curve is a curve of the form (1) Examples include the ampersand curve, bean curve, bicorn, bicuspid curve, bifoliate, bifolium, bitangent-rich curve, bow, bullet nose, butterfly curve,...
A semicubical parabola is a curve of the form (1) (i.e., it is half a cubic, and hence has power ). It has parametric equation s (2) (3) and the polar equation (4) The evolute of the...
A curve named and studied by Newton in 1701 and contained in his classification of cubic curves. It had been studied earlier by L'Hospital and Huygens in 1692 (MacTutor Archive). The curve is given by the Cartesian equation ...
A right strophoid is the strophoid of a line with pole not on and fixed point being the point where the perpendicular from to cuts is called a right strophoid. It is therefore a general strophoid with . The right strophoid...
The Ochoa curve is the elliptic curve given in Weierstrass form as The complete set of 23 integer solutions (where solutions of the form are counted as a single solution) to this equation consists of , (,...
The Ochoa curve is the elliptic curve given in Weierstrass form as The complete set of 23 integer solutions (where solutions of the form are counted as a single solution) to this equation consists of , (,...
An elliptic curve of the form for an integer. This equation has a finite number of solutions in integers for all nonzero . If is a solution, it therefore follows that is as well. Uspensky and Heaslet (1939) give elementary...
The Maltese cross curve is the cubic Algebraic curve with Cartesian equation (1) and polar equation (2) (Cundy and Rollett 1989, p. 71), so named for its resemblance to the Maltese cross. It has...
The Maclaurin trisectrix is a curve first studied by Colin Maclaurin in 1742. It was studied to provide a solution to one of the geometric problems of antiquity, in particular angle trisection, whence the name trisectrix. The...
