Write the equation of a Parabola in standard form given the focus and directrix

The video tutorial explains how to write the equation of a parabola given a focus and directrix. It covers identifying the axis of symmetry, finding the vertex, and using these to formulate the parabola equation. The tutorial emphasizes the importance of understanding the relationship between the focus, directrix, and vertex, and provides a step-by-step guide to deriving the equation.

What is the first step in writing the equation of a parabola when given a focus and a directrix?

• Plot the parabola

• Determine the vertex

• Calculate the distance between focus and directrix

• Identify the axis of symmetry

How do you find the vertex of a parabola given the focus and directrix?

• By using the distance formula

• By finding the midpoint of the y-coordinates

• By finding the midpoint of the x-coordinates

• By averaging the focus and directrix coordinates

In which direction does a parabola open?

• Away from the focus

• Parallel to the axis of symmetry

• Towards the directrix

• Towards the focus

What does the parameter 'P' represent in the equation of a parabola?

• The length of the axis of symmetry

• The distance from the vertex to the focus

• The distance from the vertex to the directrix

• The distance from the focus to the directrix

What is the final form of the parabola's equation derived in the tutorial?

• Y + 2^2 = 20(X - 4)

• Y - K^2 = 4P(X - H)

• X + 2^2 = 20(Y - 4)

• X - H^2 = 4P(Y - K)