What is the equation of a circle with center (-3,-5) and radius 4?
O A. (x+3)2 + (y + 5)2 = 4
O B. (x-3)2 + (y- 5)2 = 16
O C. (x-3)2 + (y- 5)2 = 4
O D. (x + 3)2 + (y + 5)2 = 16

  D) (x + 3)² + (y + 5)²  = 16

Step-by-step explanation:

The equation of a circle is: (x - h)² + (y - k)² = r²    

where (h, k) = center   and    r = radius

Given: (h, k) = (-3, -5)  r = 4

Equation: (x - (-3))² + (y - (-5))² = 4²

                 (x + 3)²  +  (y + 5)²  = 16

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .