Master finding the focus and directrix of a parabola with vertex at the center

The video tutorial explains how to find the directrix and focus of a parabola in conic sections, particularly when the vertex is at the origin (0,0). It covers the importance of understanding the vertex, focus, and directrix, and how these elements relate to the orientation of the parabola. The tutorial provides examples to illustrate how to determine whether a parabola opens up, down, left, or right based on the given equations. It also includes sketches to help visualize the concepts and solve problems related to parabolas in conic section form.

What do H and K represent in the context of conic sections?

• The directrix of the parabola

• The coefficients of the quadratic term

• The focus of the parabola

• The vertex of the parabola

If the value of P is negative, in which direction does the parabola open?

• Upwards

• Downwards

• To the right

• To the left

When X is squared in the equation of a parabola, how does the graph open?

• Left or right

• Up or down

• Horizontally

• Diagonally

What is the significance of the value 4P in the equation of a parabola?

• It represents the axis of symmetry

• It is the coefficient of the linear term

• It is the distance from the vertex to the focus

• It determines the width of the parabola

In the example where P is positive and the graph opens to the right, what is the focus?

• (0, 1)

• (1, 0)

• (0, 0)

• (-1, 0)

How do you determine the directrix of a parabola?

• It is parallel to the axis of symmetry

• It is always horizontal

• It is perpendicular to the axis of symmetry

• It is the same as the focus

In the example with Y^2 = -6X, what is the value of P?

• 2

• -2

• 3/2

• -3/2

What happens to the graph of a parabola if 4P is negative?

• It opens to the right

• It opens to the left

• It opens downwards

• It opens upwards

In the final example, what is the focus if P is 1/4?

• (0, 1/4)

• (1/4, 0)

• (-1/4, 0)

• (0, -1/4)

What is the directrix of a parabola with a focus at (0, 1/8)?

• Y = 1/8

• X = -1/8

• X = 1/8

• Y = -1/8