Determine the vertices, foci and center by converting an ellipse to standard form

The video tutorial explains how to rewrite an ellipse equation in standard form by completing the square. It covers identifying the center, vertices, and foci of the ellipse. The process involves factoring out coefficients, completing the square, and simplifying the equation to find key features of the ellipse.

What is the first step in rewriting an equation in standard form for an ellipse?

• Calculate the eccentricity

• Reorganize the terms

• Identify the foci

• Find the asymptotes

Why is it important to factor out coefficients when completing the square?

• To create a perfect square trinomial

• To determine the eccentricity

• To find the foci

• To simplify the equation

What is the standard form of an ellipse equation?

• (x - h)^2/a^2 + (y - k)^2/b^2 = 1

• (x - h)^2 + (y - k)^2 = r^2

• y = mx + b

• ax^2 + by^2 = c

How do you determine the center of an ellipse from its standard form?

• By finding the midpoint of the vertices

• By identifying the values of h and k

• By calculating the distance between foci

• By using the slope of the major axis

What is the relationship between a, b, and c in an ellipse?

• a^2 = b^2 - c^2

• a^2 - b^2 = c^2

• a^2 + b^2 = c^2

• a^2 = b^2 + c^2

How do you find the vertices of an ellipse?

• By adding and subtracting b from the y-coordinate

• By adding and subtracting a from the x-coordinate

• By finding the midpoint of the foci

• By using the slope of the minor axis

What is the formula to find the foci of an ellipse?

• H, K ± C

• H ± C, K

• H, K ± A

• H ± A, K