Answer: OPTION A
Step-by-step explanation:
Apply the formula for calculate the distance between two points to know the value of the diameter of the circle:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\D=\sqrt{(-5-(-5))^2+(-2-6)^2}\\D=8[/tex]
The equation of the circle is standard form is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where r is the radius and (h,k) is the point of the center of the circle.
As we know the diameter, we can find the radius:
[tex]r=\frac{8}{2}=4[/tex]
Substitute it into the equation:
[tex](x-h)^2+(y-k)^2=(4)^2[/tex]
[tex](x-h)^2+(y-k)^2=16[/tex]
Then, the answer is:
[tex](x+5)^2+(y-2)^2=16[/tex]
