Complete the square to identify foci, center, vertices and co vertices for an ellipse

The video tutorial explains the process of completing the square to find the foci, center, vertices, and co-vertices of an equation. It covers creating binomial squares, calculating the necessary C value, factoring trinomials, and solving equations. The tutorial also guides identifying the center and axes, and calculating the positions of vertices, foci, and co-vertices.

What is the primary goal of completing the square in the context of conic sections?

• To eliminate variables

• To factor the equation completely

• To simplify the equation

• To find the foci, center, vertices, and co-vertices

When creating a binomial square, what must be true about the coefficient of the squared term?

• It must be one

• It must be even

• It must be a prime number

• It must be zero

How do you determine the value of C when completing the square?

• Multiply B by two and square it

• Divide B by two and square it

• Subtract B from C

• Add B and C

What is the purpose of balancing both sides of the equation when completing the square?

• To ensure the equation remains equal

• To eliminate fractions

• To find the roots of the equation

• To simplify the equation

What is the center of the conic section after completing the square?

• (2, -3)

• (0, 0)

• (-2, 3)

• (1, 1)

How do you determine if the major axis is vertical or horizontal?

• By comparing the coefficients of x and y

• By checking the larger denominator under the squared terms

• By looking at the constant term

• By finding the midpoint of the vertices

What is the distance from the center to the vertices along the major axis?

• Square root of 7

• Square root of 2

• Square root of 5

• Square root of 3

What is the formula to find the distance to the foci from the center?

• C^2 = a^2 * b^2

• C^2 = b^2 - a^2

• C^2 = a^2 - b^2

• C^2 = a^2 + b^2

Where do the co-vertices lie in relation to the major axis?

• On the major axis

• At the center

• On the minor axis

• Outside the ellipse

What is the distance from the center to the co-vertices along the minor axis?

• Square root of 5

• Square root of 3

• Square root of 7

• Square root of 2