Quartic curves

thumb|A cardioidthumb|right|200px|The caustic (optics)|caustic appearing on the surface of this cup of coffee is a cardioid.

plane algebraic curve

quartic plane curve defined as the set (or locus) of points in the plane

right|thumb|300px|Construction of the limaçon with polar coordinates' origin at

plane curve, 3-cusped hypocycloid

plane algebraic curve

the set of points that have the same linear combination of distances from two fixed points

500px|right|thumb|Hippopede (red) given as the pedal curve of an [[ellipse (black). The equation of this hippopede is: 4x^2 + y^2 = (x^2 + y^2)^2]]

algebraic curve defined in projective plane by a quartic homogeneous polynomial

thumb|200px|right|Squircle centred on the origin () with minor radius :

algebraic curve

thumb|300px|Bicorn In geometry, the bicorn, also known as a cocked hat curve due to its resemblance to a bicorne, is a rational quartic curve defined by the equation y^2 \left(a^2 - x^2\right) = \left(x^2 + 2ay - a^2\right)^2. It has two cusps and is symmetric about the y-axis.

type of two-dimensional algebraic curve

algebraic curve

compact Riemann surface of genus 3

quartic plane curve; bicircular quartic curves that are symmetric with respect to the x and y-axes. Spiric sections are included in the family of toric sections and include the family of hippopedes and the family of Cassini ovals

intersection of a plane with a torus

plane quartic curve having 28 real bitangents

plane quartic curve of the form a²y² – b²x² = x²y²

family of elliptic curves of the form 𝑥²+𝑦²=1+𝑑𝑥²𝑦²