Answer:
[tex](x+6)^2+(y-5)^2=41[/tex]
Step-by-step explanation:
The equation of a circle follows the general equation [tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Since the center of the circle is (-6, 5), we progress to the formula equation [tex](x + 6)^2 + (y- 5)^2 = r^2[/tex]
Since this is a circle, the distance between (-6, 5) and (-1, 1) is the radius of the circle.
[tex]r = \sqrt{(-6 + 1)^2 + (5 - 1)^2} = \sqrt{5^2+4^2}=\sqrt{41}\\\\r^2 = 41[/tex]
So we can obtain the equation [tex](x+6)^2+(y-5)^2=41[/tex]
