Writing the equation of a parabola given the focus and directrix

The video tutorial explains how to plot the focus and directrix of a parabola, emphasizing the importance of labeling. It discusses the orientation of the parabola in relation to the axis of symmetry and how it opens towards the focus. The tutorial guides viewers through finding the vertex by calculating the midpoint between the focus and directrix. It explains the significance of the value P, its direction, and how it affects the parabola's equation. Finally, the video demonstrates how to write and simplify the equation of a parabola using the determined values.

What is the significance of labeling points when plotting a parabola?

What does it mean for a parabola to open towards the focus?

Explain the relationship between the focus, directrix, and vertex of a parabola.

Describe how to find the vertex of a parabola given the focus and directrix.

How do you determine the value of P in the context of a parabola?

How does the direction of P affect the orientation of the parabola?

What is the equation of a parabola in terms of H, K, and P?