How to write the equation of a parabola given focus and directrix

The video tutorial explains how to plot conic sections, focusing on the concepts of focus, directrix, and vertex. It demonstrates how to determine the vertex by finding the equidistant point between the focus and directrix. The tutorial also covers the orientation of parabolas and how to formulate their equations. The importance of plotting information to understand conic sections is emphasized throughout.

What is the role of the directrix in a conic section?

• It is a point that defines the curve.

• It is the axis of symmetry.

• It is the midpoint of the curve.

• It is a line that helps define the curve.

How is the vertex positioned in relation to the focus and directrix?

• It is at the origin.

• It is equidistant from both the focus and directrix.

• It is closer to the directrix.

• It is closer to the focus.

What does the variable 'P' represent in the context of parabolas?

• The distance from the vertex to the axis of symmetry.

• The distance from the vertex to the focus.

• The distance from the directrix to the vertex.

• The distance from the focus to the directrix.

Which formula is used to represent a parabola opening to the right or left?

• y^2 = 4px

• y = mx + b

• x^2 = 4py

• x = ay^2 + by + c

Why must the vertex and focus share the same Y coordinate?

• Because they are both on the axis of symmetry.

• Because they are both equidistant from the directrix.

• Because they are both on the directrix.

• Because they are both at the origin.