👉 In mathematics, a hyperbola is a conic section that arises in astronomy and astrophysics as solutions to Kepler's laws of planetary motion. It is named after Archimedes' father, who was known for his work on the heliocentric model of the solar system. A hyperbolically defined function is a function whose graph looks like an ellipse, but with an additional twist: it has "holes" where its derivative is zero (i.e., where the curve becomes vertical).