Answer:
[tex]\huge\boxed{Center= (-3,4) , Radius = 5\sqrt{2} }[/tex]
Step-by-step explanation:
Given equation is
[tex]x^2 + y^2 + 6x-8y - 25 = 0[/tex]
Adding 25 to both sides
[tex]x^2 + y^2 +6x-8y = 25[/tex]
Completing squares
[tex]x^2 +6x +y^2 - 8y = 25\\(x)^2-2(x)(-3) + (y)^2 - 2(x)(4) = 25[/tex]
Both of their "b" is -3 and 4 respectively
So, adding (-3)² => 9 and (4)² => 16 to both sides
[tex](x+3)^2 + (y-4)^2 = 25 + 9 + 16\\(x+3)^2 + (y-4)^2 = 50\\(x-(-3))^2 + (y-4)^2 = (5\sqrt{2)^2}[/tex]
Comparing it with [tex](x-h)^2+(y-k)^2 = r^2[/tex], where center = (h,k) and radius = r.
We get:
Center = (-3,4)
Radius = [tex]5\sqrt{2}[/tex]
