Exploring the Equation of a Circle

What is the standard form equation of a circle?

• (x - a)^2 + (y - b)^2 = r^2

• x^2 + y^2 + r^2 = 0

• x^2 + y^2 = r^2

• (x + a)^2 + (y + b)^2 = r

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

• Multiply a and b by 2

• The coefficients of x and y

• (a, b) from (x - a)^2 + (y - b)^2 = r^2

• Square root of r

In the equation (x - a)^2 + (y - b)^2 = r^2, what does 'r' represent?

• Diameter of the circle

• Circumference of the circle

• Area of the circle

• Radius of the circle

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

• 5

• -4

• 25

• 3

How do you convert a circle's equation to standard form?

• By completing the square

• Subtracting the center from both sides

• Multiplying each term by 2

• Adding r to both sides

What is the center of a circle with the equation x^2 + 2x + y^2 - 6y + 6 = 16?

• (1, -3)

• (-1, 3)

• (2, -6)

• (-2, 6)

Which of the following is a step in converting a non-standard form circle equation to standard form?

• Factoring out the greatest common factor

• Completing the square for both x and y terms

• Dividing each term by the coefficient of x^2

• Multiplying each term by the radius

What is the radius of the circle after converting x^2 - 12x + y^2 = 40 to standard form?

• 8

• 10

• 6

• sqrt(80)

After completing the square for x^2 + 6x + y^2 + 8y = -25, what is the center of the circle?

• (-6, -8)

• (6, 8)

• (3, 4)

• (-3, -4)

What is the radius of a circle whose equation is x^2 + 10x + y^2 - 8y = -41 after converting it to standard form?

• 5

• sqrt(41)

• 7

• sqrt(50)