Hyperbolas with Center (0,0) - Expii
These are the "simplest" hyperbolas. Common examples are x²/a² - y²/b² = 1 (transverse axis: x-axis), y²/a² - x²/b² = 1 (transverse axis: y-axis), and xy = k (inverse proportion graph, with transverse axis either y = x or y = -x).