Answer:
[tex](x + 4)^{2} + (y - 5)^{2} = 52[/tex]
Step-by-step explanation:
Standard form is [tex](x - h)^{2} + (y - k)^{2} = r^{2}[/tex] where (h, k) is the center and r is the radius
The diameter = [tex]\sqrt{(2 + 10)^{2} + (9 - 1)^{2} }[/tex] = [tex]\sqrt{144 + 64}[/tex] = [tex]\sqrt{208} = 4\sqrt{13}[/tex]
The radius = [tex]2\sqrt{13}[/tex] and [tex]r^{2} = 52[/tex]
The center of the circle = [tex](\frac{2 - 10}{2} , \frac{9 + 1}{2} )[/tex] = (-4, 5) = midpoint of diameter
equation is [tex](x + 4)^{2} + (y - 5)^{2} = 52[/tex]
