What are the basic characteristics of a parabola for conic sections

The video tutorial explains the characteristics of a parabola, focusing on its definition, vertex, axis of symmetry, focus, and directrix. It highlights the importance of the vertex as the maximum or minimum point and its relation to the axis of symmetry. The tutorial also covers the perpendicular nature of the directrix to the axis of symmetry and the significance of the distance from the vertex to the focus and directrix, denoted as P. The explanation includes how these distances relate to each other and the equations involved.

What is the defining characteristic of a parabola?

• It is a straight line.

• Every point is equidistant from the focus and directrix.

• It has no symmetry.

• It is a circle.

What is the vertex of a parabola?

• The point where the parabola intersects the x-axis.

• The highest or lowest point on the parabola.

• The midpoint of the directrix.

• The intersection of the parabola with the y-axis.

How is the axis of symmetry related to the vertex?

• It is perpendicular to the vertex.

• It passes through the vertex.

• It is the same as the directrix.

• It is parallel to the vertex.

What is the role of 'P' in a parabola?

• It is the length of the directrix.

• It is the angle of the parabola.

• It is the distance from the vertex to the focus or directrix.

• It determines the width of the parabola.

How are the focus and directrix positioned in relation to the axis of symmetry?

• They are parallel to the axis of symmetry.

• They are on the axis of symmetry.

• They are diagonal to the axis of symmetry.

• They are perpendicular to the axis of symmetry.