How can the asymptotes of a hyperbola be sketched from its central rectangle?

1. Build the central rectangle so its sides pass through each vertex and co-vertex. 2. Draw both diagonals of that rectangle and extend them past the corners. 3. Those extended diagonals are the asymptotes the branches approach. 4. Extending the sides instead gives lines the curve never approaches at all. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.2 The Hyperbola_