Answer:
[tex](x+1)^2+(y-1)^2=58[/tex]
Step-by-step explanation:
To find the equation of this circle, we must know the center and the radius.
We can find the radius by dividing the value of the distance formula by 2 (since [tex]r=\frac{d}{2}[/tex]):
[tex]d=\sqrt{(-3-1)^2+(6-(-4))^2}=\sqrt{116}\\r=d/2=\frac{\sqrt{116}}{2}[/tex]
We can then find the center of the circle by averaging the coordinates:
[tex]\frac{1+(-3)}{2}=-1[/tex]
[tex]\frac{-4+6}{2}=1[/tex]
Then, we substitute these values into the equation of a circle:
[tex](x-(-1))^2+(y-1)^2=(\frac{\sqrt{116}}{2})^2\\(x+1)^2+(y-1)^2=58[/tex]
