Graphing Conic Sections Part 4: Hyperbolas

The video tutorial covers hyperbolas, the last conic section, explaining their definition, properties, and equations. It compares hyperbolas to ellipses, highlighting the differences in foci and the constant difference in distances. The tutorial provides an example of a hyperbola equation, demonstrates sketching techniques, and discusses asymptotes and transformations. Key concepts include the transverse axis, vertices, and the role of a, b, and c terms in the equation.

What is the definition of a hyperbola in relation to its foci?

What is the significance of the constant difference in a hyperbola?

How does the equation of a hyperbola differ from that of an ellipse?

What do the terms 'a', 'b', and 'c' represent in the context of hyperbolas?

Describe how to find the vertices and foci of a hyperbola given its equation.

What role do asymptotes play in sketching a hyperbola?

Explain how to transform the equation of a hyperbola to find its new center.