Understanding the Equation of a Circle

This video tutorial explains how to convert the general equation of a circle into its standard form. It covers identifying the center and radius of the circle by forming perfect square trinomials. The process involves factoring and simplifying the equation, followed by graphing the circle. The tutorial provides a step-by-step approach to understanding the relationship between the general and standard forms of a circle equation.

What indicates that an equation represents a circle?

• The coefficients of x and y are different.

• The equation is quadratic in nature.

• The coefficients of x^2 and y^2 are the same.

• The equation has a linear term.

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^2 + y^2 = r^2

• x^2 + y^2 + 2hx + 2ky = r^2

How do you form a perfect square trinomial from x^2 - 6x?

• Add 3 to both sides.

• Add 6 to both sides.

• Add 9 to both sides.

• Subtract 9 from both sides.

What constant should be added to y^2 + 8y to make it a perfect square trinomial?

• 8

• 4

• 12

• 16

What is the result of factoring the trinomial x^2 - 6x + 9?

• (x - 9)^2

• (x - 3)^2

• (x - 3)(x + 3)

• (x + 3)^2

After completing the square, what is the standard form of the given circle equation?

• (x + 3)^2 + (y - 4)^2 = 20

• (x + 3)^2 + (y + 4)^2 = 20

• (x - 3)^2 + (y - 4)^2 = 20

• (x - 3)^2 + (y + 4)^2 = 20

What are the coordinates of the center of the circle in the standard form (x - 3)^2 + (y + 4)^2 = 20?

• (3, 4)

• (-3, -4)

• (-3, 4)

• (3, -4)

How is the radius of the circle determined from the equation (x - 3)^2 + (y + 4)^2 = 20?

• By taking the square root of 20

• By doubling the value of 20

• By halving the value of 20

• By taking the square of 20

What is the exact value of the radius of the circle?

• √20

• 2√5

• 5

• 4

What is the approximate decimal value of the radius of the circle?

• 4.5

• 4.47

• 3.47

• 5.47