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