Fiinding the standard form of a parabola given focus and directrix

The video tutorial explains how to determine the correct formula for a parabola using given focus and directrix. It guides through plotting these points, understanding the orientation of the parabola, and calculating the vertex. The tutorial concludes with deriving the standard form equation of the parabola, emphasizing the relationship between the focus, directrix, and vertex.

What is the first step in determining which formula to use for a parabola?

• Find the length of the latus rectum

• Calculate the vertex

• Plot the focus and directrix

• Determine the axis of symmetry

How does the parabola open if the directrix is a vertical line?

• Downwards

• To the right

• Upwards

• To the left

What is the relationship between the focus, vertex, and directrix in a parabola?

• The vertex is equidistant from the focus and directrix

• The focus and directrix are at the same point

• The focus is twice as far from the vertex as the directrix

• The directrix is always closer to the vertex than the focus

Where is the vertex located if the focus is at (2, 2) and the directrix is x = -2?

• (2, 0)

• (-2, 2)

• (2, -2)

• (0, 2)

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

• The distance from the focus to the directrix

• The distance from the vertex to the directrix

• The distance from the vertex to the axis of symmetry

• The distance from the vertex to the focus

Which form of the equation is used for a horizontal parabola?

• y^2 = 4px

• x^2 = 4py

• x^2 + y^2 = r^2

• y = mx + b

What is the final form of the equation derived for the parabola in the video?

• x = 1/8 y^2 - 1/2 y + 1/2

• y = 1/8 x^2 - 1/2 x + 1/2

• x = 1/4 y^2 - y + 1

• y = 1/4 x^2 - x + 1