Converting the Equation of a Circle from General Form to Standard Form

This video tutorial teaches how to translate the equation of a circle from general form to standard form using algebraic techniques, specifically by completing the square. It covers the concepts of binomials, perfect square trinomials, and the process of completing the square. The tutorial also explains the standard and general forms of circle equations and provides a step-by-step guide to converting between these forms.

What is a perfect square trinomial?

• A trinomial with only one term

• A trinomial that cannot be factored

• A trinomial with three different terms

• A trinomial that can be factored into two identical binomials

How can you create a perfect square trinomial from x^2 + 8x?

• Add 16

• Add 8

• Add 2

• Add 4

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

• x - h^2 + y - k^2 = r^2

• x - h^2 + y - k^2 = r^2

• x - h^2 + y - k^2 = r

• x^2 + y^2 = r^2

What is the first step in converting a circle's equation from general form to standard form?

• Move the constant to the other side

• Simplify the equation

• Complete the square

• Group the x and y terms

When completing the square for the x terms in the equation x^2 - 8x, what value is added?

• 16

• 8

• 2

• 4

What is the center of the circle given by the equation (x - 4)^2 + (y + 2)^2 = 16?

• (4, -2)

• (-4, -2)

• (4, 2)

• (-4, 2)

What is the radius of the circle with the equation (x - 4)^2 + (y + 2)^2 = 16?

• 2

• 8

• 16

• 4