Equation of Circle in Standard Form

What is the standard form of the equation of the circle 𝑥 2 + 𝑦 2 + 4𝑥 − 4𝑦 − 28 = 0?

• (𝑥 + 2) 2 + (𝑦 − 2) 2 = 36

• (𝑥 − 4) 2 + (𝑦 + 4) 2 = 28

• (𝑥 − 2) 2 + (𝑦 + 2) 2 = 36

• (𝑥 − 2) 2 + (𝑦 − 2) 2 = 28

Which of the following is the equation of a circle with radius 3 and center (-1, -4)?

• (x + 1)² + (y + 4)² = 9

• (x – 1)² + (y – 4)² = 9

• (x + 1)² + (y – 4)² = 9

• (x – 1)² + (y + 4)² = 9

Which equation represents the circle whose center is (-2, 3) and whose radius is 5?

• (x - 2)²+ (y - 3)² = 10

• (x +2)²+ (y - 3)² = 10

• (x +2)²+ (y - 3)² = 25

• (x - 2)²+ (y + 3)² = 25

The equation of the circle is (𝑥 + 3) ² + (𝑦 − 6) ² = 24. What is the radius?

• A. 3√6     

• B. 2√6

• C. 5√2

• C. 5√2

What is the equation of the circle?

• (x+1)² + (y +1)² = 3

• (x+1)² + (y -1)² = 3

• (x+1)² + (y +1)² = 9

• (x-1)² + (y -1)² = 9

What is the equation of the circle shown in the graph?

Mathematical Equivalence

ON

In the equation (x – 5)² + (y + 2)² = 16, what is the radius of a circle?

• A. 16

• B. 8

• C. 4

• D. 2

A circle has the equation (x - 3)²+ (y + 5)² = 36. Which of the following statements is NOT true?

• A. The x-coordinate of the center is 3.

• B. The y-coordinate of the center is 5.

• C. The radius of the circle is 6.

• D. The center of the circle is (3, -5).

A circle has an equation of x² + y² = 81. What is the center of a circle?

• (0, 0)

• (1, 1)

• (1, 0)

• (0, 1)

What is the general form of the equation (𝑥 − 2) 2 + (𝑦 + 5) 2 = 9?

• 𝑥 2 + 𝑦 2 + 6𝑥 − 8𝑦 + 12 = 0

• 𝑥 2 + 𝑦 2 − 4𝑥 + 10𝑦 + 20 = 0

• 𝑥 2 + 𝑦 2 + 7𝑥 − 8𝑦 + 15 = 0

• 𝑥 2 + 𝑦 2 + 3𝑥 − 2𝑦 − 4 = 0