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 role of the focus in the orientation of a parabola?

• The parabola is parallel to the focus.

• The parabola moves away from the focus.

• The parabola moves towards the focus.

• The parabola is perpendicular to the focus.

Where is the vertex located in relation to the focus and directrix?

• Midway between the focus and directrix

• At the directrix

• At the focus

• Above the directrix

What is the significance of the vertex in a parabola's equation?

• It determines the parabola's width.

• It is used to calculate the parabola's height.

• It provides the values for H and K in the equation.

• It is irrelevant to the equation.

How is the parameter P defined in the context of a parabola?

• The distance from the focus to the origin

• The distance from the vertex to the directrix

• The distance from the vertex to the focus

• The distance from the directrix to the focus

What is the correct form of the parabola's equation after simplification?

• X + 2 squared equals -8 times Y - 4

• X + 2 squared equals 8 times Y + 4

• X - 2 squared equals 8 times Y - 4

• X - 2 squared equals -8 times Y + 4