Match the circle equations in general form with their corresponding equations in standard form. x2 + y2 - 4x + 12y - 20 = 0 (x - 6) 2 + (y - 4) 2 = 56 x2 + y2 + 6x - 8y - 10 = 0 (x - 2) 2 + (y + 6) 2 = 60 3x2 + 3y2 + 12x + 18y - 15 = 0 (x + 2) 2 + (y + 3) 2 = 18 5x2 + 5y2 - 10x + 20y - 30 = 0 (x + 1) 2 + (y - 6) 2 = 46 2x2 + 2y2 - 24x - 16y - 8 = 0 x2 + y2 + 2x - 12y - 9 = 0

The equation form of a circle is (x - a) ² + (y - b) ² = r²

Equation 1:

x² - 4x + y² + 12y - 20 = 0 ⇒ use the completing the square method for x² - 4x and y² + 12y

x² - 4x = (x - 2) ² - 4

y² + 12y = (y + 6) ² - 36

Put them back together, we have

(x - 2) ² - 4 + (y + 6) ² - 36 - 20 = 0

(x - 2) ² + (y + 6) ² - 4 - 36 - 20 = 0

(x - 2) ² + (y + 6) ² - 60 = 0

(x - 2) ² + (y + 6) ² = 60

Equation 2:

x² + y² + 6x - 8y - 10 = 0

(x² + 6x) + (y² - 8y) - 10 = 0

(x + 3) ² - 9 + (y - 4) ² - 16 - 10 = 0

(x + 3) ² + (y - 4) ² - 9 - 16 - 10 = 0

(x + 3) ² + (y - 4) ² - 35 = 0

(x + 3) ² + (y - 4) ² = 35

Equation 3:

3x² + 12x + 3y² + 18y - 15 = 0

3 [x² + 4x + y² + 6y - 5] = 0

x² + 4x + y² + 6y - 5 = 0

(x² + 4x) + (y² + 6y) - 5 = 0

(x + 2) ² - 4 + (y + 3) ² - 9 - 5 = 0

(x + 2) ² + (y + 3) ² - 4 - 9 - 5 = 0

(x + 2) ² + (y + 3) ² - 18 = 0

(x + 2) ² + (y + 3) ² = 18

Equation 4:

5x² + 5y² - 10x + 20y - 30 = 0

5 [x² + y² - 2x + 4y - 6] = 0

x² + y² - 2x + 4y - 6 = 0

(x² - 2x) + (y² + 4y) - 6 = 0

(x - 1) ² - 2 + (y + 2) ² - 4 - 6 = 0

(x - 1) ² + (y + 2) ² - 2 - 4 - 6 = 0

(x - 1) ² + (y + 2) ² - 12 = 0

(x - 1) ² + (y + 2) ² = 12

Equation 5:

2x² + 2y² - 24x - 16y - 8 = 0

2 [x² + y² - 12x - 8y - 4] = 0

x² + y² - 12x - 8y - 4 = 0

(x² - 12x) + (y² - 8y) - 4 = 0

(x - 6) ² - 36 + (y - 4) ² - 16 - 4 = 0

(x - 6) ² + (y - 4) ² - 36 - 16 - 4 = 0

(x - 6) ² + (y - 4) ² - 56 = 0

(x - 6) ² + (y - 4) ² = 56

Equation 6:

x² + y² + 2x - 12y - 9 = 0

(x² + 2x) + (y² - 12y) - 9 = 0

(x + 1) ² - 1 + (y - 6) ² - 36 - 9 = 0

(x + 1) ² + (y - 6) ² - 1 - 36 - 9 = 0

(x + 1) ² + (y - 6) ² - 46 = 0

(x + 1) ² + (y - 6) ² = 46