Given the foci and length of major axis find the find the equation of an ellipse

The video tutorial explains how to find the standard equation of an ellipse. It covers determining whether the ellipse is horizontal or vertical, finding the center and foci, and calculating the values of A, B, and C. The tutorial concludes with finalizing the standard form of the ellipse equation.

What is the first step in finding the standard equation of an ellipse?

• Determine the length of the minor axis

• Identify if the ellipse is horizontal or vertical

• Calculate the area of the ellipse

• Find the eccentricity of the ellipse

What lies on the major axis of symmetry in a horizontal ellipse?

• Only the foci

• The center, foci, and vertices

• Only the center

• Only the vertices

How is the center of the ellipse determined from the foci?

• By averaging the coordinates of the foci

• By calculating the eccentricity

• By finding the midpoint of the major axis

• By using the distance formula

What is the relationship between the major axis length and 'a'?

• The major axis length is twice 'a'

• The major axis length is half of 'a'

• The major axis length is equal to 'a'

• The major axis length is three times 'a'

Which formula is used to find 'b' in the ellipse equation?

• c^2 = a^2 + b^2

• b^2 = a^2 + c^2

• a^2 = b^2 + c^2

• a^2 = c^2 - b^2

What does 'X' and 'Y' represent in the standard form of an ellipse equation?

• The vertices of the ellipse

• The foci of the ellipse

• The center of the ellipse

• All the points on the ellipse

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

• (X - 1)^2/9 + (Y - 2)^2/5 = 1

• (X - 2)^2/9 + (Y - 1)^2/5 = 1

• (X - 1)^2/5 + (Y - 2)^2/9 = 1

• (X - 2)^2/5 + (Y - 1)^2/9 = 1