What you need to know parabola in conic section

The video tutorial explains the properties of parabolas within conic sections, focusing on their orientation, vertex form, and the roles of the focus and directrix. It distinguishes between vertical and horizontal parabolas and introduces the concepts of focal length and width. The tutorial also provides guidance on identifying these elements in parabolas and offers additional resources for further learning on ellipses and hyperbolas.

What determines whether a parabola opens vertically or horizontally?

• The value of H and K

• The variable that is squared

• The axis of symmetry

• The distance from the vertex to the focus

In the context of parabolas, what is the role of the vertex?

• It is the point where the parabola changes direction

• It is the intersection of the parabola with the x-axis

• It determines the width of the parabola

• It is the midpoint of the parabola

What is the focus of a parabola?

• A line parallel to the axis of symmetry

• A point inside the parabola equidistant from the directrix

• The highest or lowest point on the parabola

• The intersection of the parabola with the y-axis

How do you find the directrix of a vertical parabola?

• By using the formula y = K ± P

• By using the formula x = H ± P

• By finding the midpoint between the vertex and the focus

• By calculating the distance from the vertex to the axis of symmetry

What is the focal length in the context of parabolas?

• The distance from the vertex to the directrix

• The distance from the vertex to the focus

• The width of the parabola at its widest point

• The length of the axis of symmetry

For a horizontal parabola, how is the focus determined?

• By adding P to the Y coordinate of the vertex

• By subtracting P from the X coordinate of the vertex

• By adding P to the X coordinate of the vertex

• By subtracting P from the Y coordinate of the vertex

What is the focal width of a parabola?

• The length of the axis of symmetry

• The distance between the directrix and the focus

• The width of the parabola at the focus

• The distance from the vertex to the focus