Mastering Ellipse Equations through Completing the Square

What is the main topic of the video presented by Terry van Noy?

• Ellipse Equations

• Hyperbola Equations

• Parabola Equations

• Circle Equations

What is the purpose of completing the square in algebra?

• To find the roots of a quadratic equation

• To simplify linear equations

• To form a perfect square trinomial

• To solve cubic equations

In the context of an ellipse, what do the H and K values represent?

• The center of the ellipse

• The vertices of the ellipse

• The foci of the ellipse

• The width and height of the ellipse

What is the first step in solving an ellipse equation by completing the square?

• Divide both sides by the same number

• Move the constant term to the right side

• Factor out the greatest common factor

• Square the middle term

When completing the square, what do you do after taking half of the middle term?

• Subtract it from both sides

• Multiply it by the leading coefficient

• Square it

• Add it to both sides

In the standard form of an ellipse, what does the A value represent?

• The height of the ellipse

• The width of the ellipse

• The center of the ellipse

• The distance between the foci

What is the result of factoring out the greatest common factor from the X group in the first example problem?

• x^2 - 4x

• x^2 - 8x

• x^2 - 2x

• x^2 - 6x

In the first example problem, what is the value added to both sides after completing the square for the X group?

• 113

• 64

• 49

• 16

In the second example problem, what is the greatest common factor factored out from the Y group?

• 8

• 16

• 9

• 4

What is the final form of the equation in the second example problem?

• (x-4)^2/16 + (y-4)^2/8 = 1

• (x-4)^2/8 + (y-4)^2/16 = 1

• (x-4)^2/9 + (y-4)^2/16 = 1

• (x-4)^2/16 + (y-4)^2/9 = 1