Fermat’s hyperbola

Fermat's hyperbola refers to a generalization of the rectangular hyperbola, xy = a², to the form a^n-1y = xⁿ. These curves are known as the parabolas of Fermat if n is positive and hyperbolas of Fermat if n is negative.1

This generalization was part of Pierre de Fermat's work on analyzing curves and equations. He developed methods that were equivalent to differentiation and integration, allowing him to find tangents to curves and areas bounded by them. While Fermat's name is most famously associated with Fermat's Last Theorem, his contributions also extended to analytic geometry, calculus, and number theory.12