Understanding Parabolas: Focus and Directrix

The video tutorial explains how to find the equation of a parabola given its focus and directrix. It starts by plotting the focus and directrix, then discusses the properties of parabolas, including the significance of the 'p' value. The tutorial guides viewers through calculating the vertex and deriving the equation, ensuring the parabola opens in the correct direction. Finally, it confirms the equation by plotting the vertex and checking its position relative to the focus and directrix.

What is the focus of the parabola in the given problem?

• (-6, 2)

• (6, -2)

• (2, -6)

• (-2, 6)

What is the equation of the directrix in the problem?

• y = -4

• x = -4

• y = 4

• x = 4

In which direction does the parabola open?

• Downwards

• Right

• Upwards

• Left

What is the general form of the parabola's equation?

• (y - H)^2 = 4P(x - K)

• (x - H)^2 = 4P(y - K)

• (y - K)^2 = 4P(x - H)

• (x - K)^2 = 4P(y - H)

How is the distance between the focus and directrix related to 'p'?

• 2|p|

• |p|

• 4|p|

• |p|/2

What is the value of 'p' for the parabola?

• 10

• -5

• -10

• 5

How is the vertex of the parabola determined?

• By moving 5 units to the right of the focus

• By moving 5 units to the left of the focus

• By moving 5 units above the focus

• By moving 5 units below the focus

What are the coordinates of the vertex?

• (-2, 1)

• (2, -1)

• (-1, 2)

• (1, -2)

What is the final equation of the parabola?

• (x + 2)^2 = 20(y - 1)

• (x - 2)^2 = 20(y + 1)

• (x + 2)^2 = 10(y - 1)

• (x - 2)^2 = 10(y + 1)

What is the significance of the vertex in relation to the focus and directrix?

• It is equidistant from both

• It is closer to the focus

• It is closer to the directrix

• It is not related to either