Understanding Parabolas

The video tutorial explains how to find the equation of a parabola given its focus and directrix. It starts by plotting the focus and sketching the directrix, then discusses the properties of parabolas, including the role of 'p' in determining the direction of opening. The tutorial calculates the distance from the directrix to the focus to find 'p' and the vertex. Finally, it derives and simplifies the equation of the parabola, ensuring it opens in the correct direction.

What are the coordinates of the focus given in the problem?

• (2, -3)

• (2, 3)

• (-2, 3)

• (3, 2)

Which direction does the parabola open based on the given focus and directrix?

• To the right

• Upward

• Downward

• To the left

What is the general form of the equation for a parabola that opens to the right?

• (x - h)^2 = 4p(y - k)

• (y - k)^2 = 4p(y - h)

• (y - k)^2 = 4p(x - h)

• (x - h)^2 = 4p(x - k)

What is the relationship between the vertex, focus, and directrix in terms of distance?

• The vertex is not related to the focus and directrix

• The vertex is closer to the directrix

• The vertex is closer to the focus

• The vertex is equidistant from the focus and directrix

How do you calculate the value of p given the focus and directrix?

• Subtract the y-coordinates

• Add the x-coordinates

• Add the y-coordinates

• Subtract the x-coordinates

What is the value of p in this problem?

• 8

• 2

• 4

• 6

How do you determine the vertex of the parabola?

• By subtracting p from the directrix

• By adding p to the directrix

• By subtracting p from the focus

• By adding p to the focus

What are the coordinates of the vertex in this problem?

• (-3, 2)

• (-2, 3)

• (2, 3)

• (3, -2)

What is the final equation of the parabola derived in the problem?

• (y - 3)^2 = 16(x + 2)

• (x - 3)^2 = 16(y + 2)

• (y + 3)^2 = 16(x - 2)

• (x + 3)^2 = 16(y - 2)

Why is the value of p positive in this problem?

• Because the parabola opens to the left

• Because the parabola opens downward

• Because the parabola opens upward

• Because the parabola opens to the right