Find the equation of an ellipse

The video tutorial explains how to determine the major axis of an ellipse by plotting vertices and using the ellipse formula. It covers the process of calculating B squared and finalizing the equation of the ellipse, with the center at the origin. The tutorial provides a step-by-step approach to solving the problem, ensuring a clear understanding of the geometric concepts involved.

What is the first step in determining the orientation of the major axis of an ellipse?

• Calculate the distance between the foci

• Plot the vertices and check their alignment

• Find the midpoint of the vertices

• Determine the length of the minor axis

Which formula is used for an ellipse with a vertical major axis?

• (x - h)^2 / c^2 + (y - k)^2 / d^2 = 1

• (x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

• (x - h)^2 / b^2 + (y - k)^2 / a^2 = 1

• (x - h)^2 + (y - k)^2 = r^2

What is the value of 'a' if the distance from the center to the vertices is 5?

• 0

• 25

• 5

• 10

How do you simplify the equation after substituting known points into the ellipse formula?

• By solving for B^2

• By multiplying the terms

• By adding the coordinates

• By dividing by the center coordinates

What is the next step after simplifying the equation to solve for B^2?

• Divide by the coefficient of B^2

• Add the terms on both sides

• Multiply by the reciprocal of the coefficient

• Subtract the constant term

What is the final value of B^2 in the ellipse equation?

• 25

• 21/400

• 16

• 400/21

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

• x^2 / 25 + y^2 / (400/21) = 1

• x^2 / (400/21) + y^2 / 25 = 1

• x^2 / 25 + y^2 / 16 = 1

• x^2 / 16 + y^2 / 25 = 1