Master Writing the equation of a parabola given the vertex, focus or directrix

The video tutorial explains how to write the equation of a parabola using given information such as the vertex, focus, and directrix. It emphasizes the importance of knowing the vertex coordinates (H, K) and the value of P, which is the distance from the vertex to the focus or directrix. The tutorial includes multiple examples demonstrating how to plot the given information, determine the direction of the parabola, and solve for the equation in both conic and standard forms.

What are the essential components needed to write the equation of a parabola?

• Vertex and directrix

• Focus and directrix

• Vertex and distance P

• Vertex and focus

How does the vertex of a parabola relate to its focus?

• The vertex is always to the left of the focus

• The vertex is always above the focus

• The vertex is always below the focus

• The vertex is always at the midpoint between the focus and directrix

In which direction does a parabola open if its vertex is at (2, -3) and its focus is at (2, -5)?

• Left

• Downwards

• Upwards

• Right

What is the standard form of a parabola's equation if it opens downwards?

• x^2 = 4p(y - k)

• x^2 = -4p(y - k)

• y^2 = 4p(x - h)

• y^2 = -4p(x - h)

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

• The vertex is at the focus

• The vertex is at the origin

• The vertex is at the directrix

• The vertex is at the midpoint between the focus and directrix

If a parabola has a vertical directrix, in which direction does it open?

• It does not open

• Left or right

• Downwards

• Upwards

What is the value of P if the vertex is at (0, 3) and the directrix is y = 2/3?

• -7/3

• -2/3

• 2/3

• 7/3

How do you determine the direction of a parabola with a horizontal axis of symmetry?

• By the sign of P

• By the position of the vertex

• By the position of the focus

• By the equation of the directrix

What is the equation of a parabola with vertex (2, 7) and focus (-2, 7)?

• (x + 2)^2 = 16(y - 7)

• (x - 2)^2 = -16(y - 7)

• (y - 7)^2 = 16(x + 2)

• (y - 7)^2 = -16(x - 2)

What is the significance of the value of P in the equation of a parabola?

• It determines the length of the directrix

• It determines the vertex position

• It determines the direction the parabola opens

• It determines the width of the parabola