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 purpose of labeling points when plotting a parabola?

• To ensure the graph is symmetrical

• To avoid confusion with multiple points

• To highlight the directrix

• To make the graph look colorful

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

• At the directrix

• At the origin

• At the focus

• At the midpoint between the focus and directrix

What does the variable 'P' represent in the context of a parabola?

• The distance from the focus to the origin

• The distance from the vertex to the focus

• The distance from the vertex to the directrix

• The total distance from the focus to the directrix

How does the direction of the parabola affect the value of 'P'?

• It makes 'P' always positive

• It determines the sign of 'P'

• It makes 'P' always negative

• It has no effect on 'P'

What is the significance of the opposite of 'P' in a parabola?

• It shows the distance from the focus to the vertex

• It shows the distance from the vertex to the directrix

• It indicates the parabola opens downwards

• It indicates the parabola opens upwards

Which conic section equation is used for a parabola opening to the left?

• Vertical conic section

• Elliptical conic section

• Horizontal conic section

• Circular conic section

What is the final equation of the parabola discussed in the tutorial?

• y - 2 squared equals 4 times x + 2

• y - 2 squared equals -4 times x + 2

• x - 2 squared equals 4 times y + 2

• x - 2 squared equals -4 times y + 2