How to write the equation of a parabola given the focus and directrix

The video tutorial explains the concepts of focus and directrix in relation to parabolas. It guides students through determining the orientation of a parabola, finding the vertex, and formulating the equation. The tutorial emphasizes the importance of understanding the relationship between the focus, directrix, and vertex, and provides a step-by-step approach to simplifying the parabola equation.

What is the definition of the focus in relation to a parabola?

Explain the relationship between the focus, directrix, and the direction of the parabola.

How do you determine the vertex of a parabola given the focus and directrix?

What is the significance of the value P in the context of a parabola?

Describe how to derive the equation of a parabola using the focus and vertex.