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

The video tutorial explains how to write the equation of a parabola with a vertex at the origin, given either the focus or the directrix. It covers the importance of understanding the value of P, which represents the distance from the vertex to the focus or directrix, and how the direction of P affects the parabola's orientation. The tutorial includes examples of both horizontal and vertical parabolas, demonstrating how to plot given information and solve for the parabola's equation in both conic section and standard forms.

What does the variable P represent in the context of a parabola?

• The slope of the parabola

• The coordinates of the vertex

• The distance from the vertex to the focus

• The distance from the vertex to the directrix

If the focus of a parabola is to the right of the vertex, in which direction does the parabola open?

• Downwards

• Upwards

• To the right

• To the left

How do you determine the value of P when given the focus of a parabola?

• By using the equation of the directrix

• By calculating the midpoint between the vertex and the focus

• By measuring the distance from the vertex to the focus

• By measuring the distance from the vertex to the directrix

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

• They are perpendicular to each other

• They are the same line

• They are parallel to each other

• They intersect at the vertex

When given a vertical directrix, in which direction does the parabola open?

• Only upwards

• Upwards or downwards

• Only downwards

• To the left or right

What is the significance of converting a parabola's equation into standard form?

• It simplifies the calculation of the focus

• It is required for solving quadratic equations

• It makes the equation easier to graph

• It helps in identifying the vertex

If a parabola has a horizontal directrix, what can be inferred about its axis of symmetry?

• It is circular

• It is horizontal

• It is diagonal

• It is vertical