12 points! pls .
drag the tiles to the boxes to form correct pairs. not all tiles will be used.
match the circle equations in general form with their corresponding equations in standard form.

1) x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

2) x² + y² + 6x - 8y - 10 = 0 ⇒ No choice

3) 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

4) 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ No choice

5) 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

6) x² + y² + 2x - 6y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Step-by-step explanation:

- The general form of the equation of the circle is:

* x² + y² + Dx + Ey + F = 0

 where D , E and F are constant

- The standard form of the equation of the circle is:

* (x - h)² + (y - k)² = r²

 where (h , k) is the center of the circle, r is the radius of it

- To chose the circle equations in general form with their

  corresponding equations in standard form lets do that

1) x² + y² - 4x + 12y - 20 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(-4)/2(1) = 2

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(12)/2(1) = -6

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (2)² + (-6)² - (-20) = 4 + 36 + 20 = 60

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x - 2)² + (y + 6)² = 60 ⇒ x² + y² - 4x + 12y - 20 = 0

2) x² + y² + 6x - 8y - 10 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(6)/2(1) = -3

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(-8)/2(1) = 4

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (-3)² + (4)² - (-10) = 9 + 16 + 10 = 35

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x + 3)² + (y - 4)² = 35 ⇒ there is no choice

3) 3x² + 3y² + 12x + 18y - 15 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(12)/2(3) = -2

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(18)/2(3) = -3

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (-2)² + (-3)² - (-15/3) = 4 + 9 + 5 = 18

- We divide F by 3 because the coefficient of x² and y²

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x + 2)² + (y + 3)² = 18 ⇒ 3x² + 3y² + 12x + 18y - 15 = 0

4) 5x² + 5y² - 10x + 20y - 30 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(-10)/2(5) = 1

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(20)/2(5) = -2

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (1)² + (-2)² - (-30/5) = 1 + 4 + 6 = 11

- We divide F by 5 because the coefficient of x² and y²

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x - 1)² + (y + 2)² = 11 ⇒ there is no choice

5) 2x² + 2y² - 24x - 16y - 8 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(-24)/2(2) = 6

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(-16)/2(2) = 4

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (6)² + (4)² - (-8/2) = 36 + 16 + 4 = 56

- We divide F by 2 because the coefficient of x² and y²

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x - 6)² + (y - 4)² = 56 ⇒ 2x² + 2y² - 24x - 16y - 8 = 0

6) x² + y² + 2x - 12y - 9 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(2)/2(1) = -1

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(-12)/2(1) = 6

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (-1)² + (6)² - (-9) = 1 + 36 + 9 = 46

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x + 1)² + (y - 6)² = 46 ⇒ x² + y² + 2x - 6y - 9 = 0