Answer:
[tex]r^{2}=(x+5)^{2}+(y-4)^{2}[/tex]
Step-by-step explanation:
we know that
The equation of the circle into center-radius form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center of the circle
r is the radius of the circle
Step 1
we have
[tex]A(-8,2)\\B(-2,6)[/tex]
Find the center of the circle
The center of the circle is the midpoint between point A and point B
The formula to calculate the midpoint is equal to
[tex]M(\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]
substitute the values
[tex]M(\frac{-8-2}{2} ,\frac{2+6}{2})[/tex]
[tex]M({-5 ,4)[/tex]
the equation of the circle is equal to
[tex](x+5)^{2}+(y-4)^{2}=r^{2}[/tex]
