Write the equation of an ellipse with the given vertices & passes through a point

The video tutorial explains how to determine the equation of an ellipse by first identifying the type of ellipse based on the position of its vertices. The instructor plots the vertices, identifies the major axis, and sets up the equation for a vertical ellipse. The process involves solving for B^2 using a random point on the ellipse and deriving the final equation. The tutorial emphasizes understanding the relationship between the vertices, center, and co-vertices, and how to use this information to form the standard equation of an ellipse.

What is the major axis of the ellipse if the vertices are (0,5) and (0,-5)?

• Diagonal

• None

• Vertical

• Horizontal

Which part of the ellipse equation does the distance from the center to a vertex correspond to?

• X term

• Y term

• A term

• B term

What does the variable B represent in the context of an ellipse?

• Distance from vertex to foci

• Distance from center to foci

• Distance from center to co-vertex

• Distance from center to vertex

How can you solve for B^2 in the ellipse equation?

• By using the distance from center to vertex

• By using a random point on the ellipse

• By using the distance from vertex to co-vertex

• By using the distance from center to foci

What is the final form of the ellipse equation derived in the video?

• X^2/19 + Y^2/25 = 1

• X^2/5 + Y^2/19 = 1

• X^2/19 + Y^2/5 = 1

• X^2/25 + Y^2/19 = 1