Deriving and Using the Equation of a Circle Quiz

Question 1: Derive the equation of a circle with center (3, -4) and radius 5.

• (x + 3)^2 + (y - 4)^2 = 25

• (x - 3)^2 + (y - 4)^2 = 25

• (x - 3)^2 + (y + 4)^2 = 25

• (x - 3)^2 - (y + 4)^2 = 25

Question 2: Derive the equation of a circle with center (-2, 1) and radius 7.

• (x + 2)^2 + (y - 1)^2 = 49

• (x - 2)^2 + (y - 1)^2 = 7

• (x - 2)^2 + (y + 1)^2 = 49

• (x + 1)^2 + (y - 2)^2 = 49

Question 3: Derive the equation of a circle with center (0, 0) and radius 9.

• x^2 - y^2 = 81

• x^2 - y^2 = 9

• x^2 + y^2 = 9

• x^2 + y^2 = 81

Question 4: Derive the equation of a circle with center (5, 2) and radius 6.

• (x - 5)^2 + (y - 2)^2 = 36

• (x + 5)^2 + (y + 2)^2 = 36

• (x - 2)^2 + (y - 5)^2 = 36

• (x - 5)^2 + (y - 2)^2 = 6

Question 5: Identify the center of the circle with equation x^2 + y^2 - 6x + 8y + 9 = 0.

• (3, -4)

• (0, 0)

• (2, 4)

• (5, -2)

Question 6: Identify the center of the circle with equation x^2 + y^2 + 4x - 10y - 25 = 0.

• (0, 0)

• (-2, 5)

• (-4, 10)

• (3, -5)

Question 7: Identify the center of the circle with equation x^2 + y^2 - 2x - 4y + 4 = 0.

• (1, 2)

• (0, 0)

• (3, 4)

• (2, 1)

Question 8: Find the radius of the circle with equation x^2 + y^2 - 8x + 6y + 9 = 0.

• 10

• 7

• 5

• 3

Question 9: Find the radius of the circle with equation x^2 + y^2 - 10x - 4y + 25 = 0.

• 2

• 7

• 3

• 5

Question 10: Find the radius of the circle with equation x^2 + y^2 + 6x - 12y + 36 = 0.

• 5

• 10

• 3

• 7