Dive into an in-depth exploration of conic sections, focusing specifically on ellipses and hyperbolas in this comprehensive 58-minute lecture. Learn the fundamental properties, equations, and graphical representations of these important geometric shapes. Gain a solid understanding of how to identify, analyze, and manipulate ellipses and hyperbolas in various mathematical contexts. This lecture, part of a broader intermediate algebra series, provides essential knowledge for students advancing their mathematical skills and preparing for more advanced topics in geometry and calculus.