What is the definition of a parabola for CONIC sections

The video tutorial explains the basic definition of a parabola, focusing on its U-shape and the role of the vertex and focus. It describes how the distance from the focus to any point on the parabola is equidistant to the directrix. The tutorial also touches on the properties of parabolas in conic sections, including their ability to open in different directions.

What is the basic definition of a parabola?

Explain the significance of the vertex in a parabola.

What role does the focus play in the definition of a parabola?

Describe the relationship between the focus, directrix, and any point on the parabola.

How does the definition of a parabola extend to conic sections beyond just quadratics?