Answer:
1.  x² + y² + 8x - 14y - 35 = 0
2.  x² + y² - 2x - 8y - 47 = 0
3.  x² + y² - 4x - 2y - 116 = 0
4.  x² + y² + 2x + 4y - 20 = 0
5.  x² + y² - 4x - 8y - 52 = 0
Step-by-step explanation:
General equation of a circle is:  x² + y² + 2gx + 2fy + c = 0
with center (-g, -f) and radius √(g² + f² - c)
1.  From inspection:  center (-4, 7)  and radius = √100 = 10
  Therefore, g = 4  and  f = -7
  √(4² + (-7)² - c) = 10  ⇒  65 - c = 100  ⇒  c = -35
  So,  x² + y² + 8x - 14y - 35 = 0
2.  From inspection:  center (1, 4)  and radius = √64 = 8
  Therefore, g = -1  and  f = -4
  √((-1)² + (-4)² - c) = 8  ⇒  17 - c = 64  ⇒  c = -47
  So,  x² + y² - 2x - 8y - 47 = 0
3.  From inspection:  center (2, 1)  and radius = √(11²) = 11
  Therefore, g = -2  and  f = -1
  √((-2)² + (-1)² - c) = 11  ⇒  5 - c = 121  ⇒  c = -116
  So,  x² + y² - 4x - 2y - 116 = 0
4.  From inspection:  center (-1, -2)  and radius = √25 = 5
  Therefore, g = 1  and  f = 2
  √(1² + 2² - c) = 5  ⇒  5 - c = 25  ⇒  c = -20
  So,  x² + y² + 2x + 4y - 20 = 0
5.  From inspection:  center (2, 4)  and radius = √72
  Therefore, g = -2  and  f = -4
  √((-2)² + (-4)² - c) = √72  ⇒  20 - c = 72  ⇒  c = -52
  So,  x² + y² - 4x - 8y - 52 = 0
