Completing the Square for Ellipses

The video tutorial explains how to use the method of completing the square to rewrite a conic section equation in standard form. It begins by breaking down the equation into X and Y components, factoring out constants, and completing the square for the Y terms. The tutorial then demonstrates how to find the perfect square and adjust the equation accordingly. The equation is identified as an ellipse, and the video concludes with a brief sketch of the ellipse and a summary of the solution.

What is the first step in completing the square for conic sections?

• Combine all terms into one side of the equation.

• Break up the X and Y terms.

• Multiply the entire equation by a constant.

• Graph the equation immediately.

Why can the term 9x squared be left alone in the equation?

• It is not needed for the solution.

• It is already a perfect square.

• It has a coefficient of 9.

• It is part of the Y terms.

What is the purpose of factoring out the constant from the Y terms?

• To change the equation to standard form.

• To prepare for completing the square.

• To eliminate the Y terms.

• To simplify the equation.

How do you determine the value to add for completing the square?

• Subtract the middle term from the constant.

• Multiply the middle term by 2.

• Divide the middle term by 2 and square it.

• Add the middle term to itself.

What type of conic section is identified in the video?

• Parabola

• Circle

• Hyperbola

• Ellipse

What is the final step in transforming the equation to standard form?

• Add all terms together.

• Multiply the equation by a factor.

• Divide everything by the constant.

• Subtract the constant from both sides.

What is the significance of setting the equation equal to one?

• It is necessary for graphing.

• It helps identify the conic section.

• It simplifies the equation.

• It is a step in completing the square.

What is the center of the ellipse described in the video?

• (1, 1)

• (0, 1)

• (1, 0)

• (0, 0)

What is the radius in the x-direction for the ellipse?

• 1

• 2

• 3

• 4

What is the radius in the y-direction for the ellipse?

• 3

• 4

• 2

• 1