Step-by-step explanation:
The standard equation of a circle is [tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Center = (h, k)
#1
Center = (0,2)
h = 0
k = 2
r = 5
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
[tex](x - 0)^2 + (y - 2)^2 = 5^2[/tex]
#2
Center = (-4,-5)
h = -4
k = -5
r = [tex]\sqrt{2}[/tex]
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
[tex](x - (-4))^2 + (y - (-5))^2 = \sqrt{2}^2[/tex]
[tex](x + 4))^2 + (y + 5))^2 = \sqrt{2}^2[/tex]
#3
Center =(-1,3)
h = -1
k = 3
r = 8
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
[tex](x - (-1))^2 + (y - 3)^2 = 8^2[/tex]
[tex](x + 1)^2 + (y - 3)^2 = 8^2[/tex]
#4
Center: (9,0)
h = 9
k = 0
r = [tex]\sqrt{3}[/tex]
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
[tex](x - 9)^2 + (y - 0)^2 = \sqrt{3}^2[/tex]
