Find the center and radius of a circle by completing the square

The video tutorial explains how to convert a general form equation into a standard form by completing the square. It covers grouping terms, finding the value to complete the square, and balancing the equation. The process results in perfect square trinomials that can be factored into binomial squares. The tutorial also explains how to identify the center and radius of the equation in standard form.

What is the first step in transforming a general form equation into a standard form?

• Subtract the constant from both sides

• Multiply all terms by 2

• Group the X and Y terms

• Add a constant to both sides

How do you determine the value needed to complete the square for a term?

• Subtract the constant term from the linear term

• Add the coefficients of the quadratic and linear terms

• Divide the coefficient of the linear term by 2 and square it

• Multiply the coefficient of the linear term by 2

Why is it necessary to add the same value to both sides of the equation when completing the square?

• To eliminate the constant term

• To factor the equation easily

• To ensure the equation remains balanced

• To simplify the equation

What is the standard form of a circle's equation?

• X^2 - Y^2 = R^2

• (X + H)^2 + (Y + K)^2 = R^2

• (X - H)^2 + (Y - K)^2 = R^2

• X^2 + Y^2 = R^2

How do you find the radius of a circle from its standard form equation?

• It is the sum of the coefficients of X and Y

• It is the square root of the constant on the right side

• It is the coefficient of the X term

• It is the constant term on the left side