Answer:
[tex](x+5)^2+(y+1)^2=104.[/tex]
Step-by-step explanation:
1) the equation of the circle is: (x-x₀)²+(y-y₀)²=r², where point(x₀;y₀) - centre of the circle, r - radius of the circle.
2) the coordinates of the centre are:
[tex]x_0=\frac{-4-6}{2} =-5;[/tex]
[tex]y_0=\frac{4-6}{2}=-1;[/tex]
3) the radius is the distance between (-5;-1) and (-4;-6):
[tex]r^2=\sqrt{(-4+6)^2+(-6-4)^2}=\sqrt{104};[/tex]
4) finally, the required equation is:
(x+5)²+(y+1)²=(√104)².
