Find the foci vertices and center of an ellipse by completing the square

The video tutorial explains how to transform a given equation into conic section form by completing the square. It covers the process of grouping terms, factoring out coefficients, and creating perfect square trinomials. The tutorial also demonstrates how to identify the center, vertices, and foci of the conic section, providing a step-by-step guide to understanding the transformation and properties of conic sections.

Why is it important to have the equation in conic section form?

• It is required for solving linear equations.

• It allows for easier differentiation.

• It simplifies the graphing process.

• It makes it easier to find the center and coefficients.

What must be true about the coefficient of the quadratic term before completing the square?

• It must be zero.

• It must be one.

• It must be a positive integer.

• It must be a negative integer.

When completing the square, what operation is performed on the linear term?

• Divide by two and square it.

• Subtract two and square it.

• Add two and square it.

• Multiply by two and square it.

What is the purpose of creating a perfect square trinomial?

• To simplify the equation.

• To balance the equation.

• To eliminate the linear term.

• To factor the equation easily.

How is the center of the conic section determined from the equation?

• By identifying the coefficients of x and y.

• By finding the midpoint of the vertices.

• By using the constants in the binomial squares.

• By calculating the average of a and b.

Which axis is the major axis if a^2 is under the x term?

• Vertical axis

• None of the above

• Horizontal axis

• Diagonal axis

How are the vertices of the conic section calculated?

• By adding and subtracting a from the x-coordinate of the center.

• By adding and subtracting b from the y-coordinate of the center.

• By using the midpoint formula.

• By adding and subtracting c from both coordinates of the center.