Exploring the Equation of a Circle

The video tutorial covers the equation of a circle and the method of completing the square. It begins with a review of completing the square to form a perfect square trinomial. The tutorial then explains the equation of a circle with a center at (h, k) and radius r. Through examples, the process of completing the square for both x and y terms is demonstrated, leading to the formation of the circle's equation. The video concludes with a final example and encourages further practice.

What is the purpose of completing the square in algebra?

• To form a perfect square trinomial

• To solve quadratic equations

• To graph linear equations

• To simplify expressions

What is the equation of a circle centered at (h, k) with radius r?

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r

• (x + h)^2 + (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

How do you complete the square for the expression x^2 - 6x + 9?

• (x - 6)^2

• (x - 3)^2

• (x + 3)^2

• (x + 6)^2

What is the center of a circle with the equation (x + 3)^2 + (y + 4)^2 = 25?

• (-3, -4)

• (-3, 4)

• (3, 4)

• (3, -4)

What is the radius of a circle whose equation is (x + 3)^2 + (y + 4)^2 = 25?

• 5

• 50

• 10

• 25

How many times do you complete the square for the circle's equation?

• Once

• Twice

• Three times

• Four times

After completing the square, what is the center of the circle in the equation (x + 1)^2 + (y - 3)^2 = 4?

• (-1, -3)

• (1, 3)

• (-1, 3)

• (1, -3)

What is the new form of the equation after completing the square for x^2 + 2x + 1?

• (x + 1)^2

• (x - 1)^2

• (x - 2)^2

• (x + 2)^2

What is the radius of the circle with the equation (x - 2)^2 + (y + 5)^2 = 16?

• 8

• 2

• 4

• 16

What is the center of the circle described by the equation (x - 2)^2 + (y + 5)^2 = 16?

• (2, -5)

• (-2, 5)

• (2, 5)

• (-5, 2)