Fermat’s parabola

Fermat's parabola refers to a generalization of the standard parabola equation, formulated by mathematician Pierre de Fermat. He extended the equation y = x² to the form aⁿ⁻¹y = xⁿ. These curves are known as Fermat's parabolas when n is positive.

Fermat, a 17th-century French mathematician, is considered a founder of modern number theory and made significant contributions to analytic geometry and calculus. His work on curves, including generalizations of the parabola and spiral, led to algorithms equivalent to differentiation and integration.1

The standard parabola, defined as the set of points equidistant from a fixed line (directrix) and a fixed point (focus), has applications in optics and engineering, such as in telescopes and satellite dishes. Fermat's generalization expanded the study of these curves within the framework of analytic geometry.21