Answer:
[tex](x + 1)^{2} + (y + 11)^{2} = 34[/tex]
Step-by-step explanation:
First find the midpoint of the segment from (2, -6) to (-4, -16)
((2 - 4)/2, (-6 - 16)/2)
(-2/2, -22/2)
(-1, -11) is the midpoint and is the center of the circle
Now find the distance between the 2 given points and divide by 2 to get the radius of the circle
d = [tex]\sqrt{(2 + 4)^{2} + (-6 + 16)^{2} }[/tex]
= [tex]\sqrt{6^{2} + 10^{2} }[/tex]
= [tex]\sqrt{36 + 100}[/tex]
= [tex]\sqrt{136}[/tex]
r = [tex]\sqrt{136}[/tex]/2
[tex]r^{2}[/tex] = 136/4 = 34
Equation of circle with center at (-1, -11) and radius = [tex]\sqrt{34}[/tex] is
[tex](x + 1)^{2} + (y + 11)^{2} = 34[/tex]
