Graph and write the equation of the parabola given the focus and directrix

The video tutorial explains how to write the equation of a parabola given its focus and directrix. It begins by identifying the type of parabola and its axis of symmetry through plotting. The vertex is calculated as the midpoint between the focus and directrix. The tutorial then demonstrates how to formulate the parabola equation using the vertex and focus, concluding with a summary of the process.

What is the first step in identifying the type of parabola when given the focus and directrix?

• Plot the focus and directrix to determine the axis of symmetry

• Find the midpoint between the focus and directrix

• Calculate the distance between the focus and directrix

• Directly write the equation using the focus

How is the vertex of a parabola determined when given the focus and directrix?

• It is the midpoint between the focus and directrix

• It is the same as the directrix

• It is twice the distance from the focus to the directrix

• It is the same as the focus

What is the relationship between the vertex and the axis of symmetry in a parabola?

• The vertex is always below the axis of symmetry

• The vertex is always above the axis of symmetry

• The vertex lies on the axis of symmetry

• The vertex is perpendicular to the axis of symmetry

Which formula represents the equation of a parabola with a vertical axis of symmetry?

• Y - K = 4P(X - H)^2

• X - H = 4P(Y - K)^2

• X - H = 4P(Y + K)^2

• X + H = 4P(Y - K)^2

How do you calculate the value of 'P' in the parabola's equation?

• By finding the distance from the vertex to the origin

• By finding the distance from the vertex to the focus

• By finding the distance from the vertex to the directrix

• By finding the distance from the focus to the directrix