Question

Explain How you got that answer

Answer 1

`\huge\boxed{Center= (-3,4) , Radius = 5√(2) }`

Explanation:

Given equation is

`x^2 + y^2 + 6x-8y - 25 = 0`

Adding 25 to both sides

`x^2 + y^2 +6x-8y = 25`

Completing squares

`x^2 +6x +y^2 - 8y = 25\\(x)^2-2(x)(-3) + (y)^2 - 2(x)(4) = 25`

Both of their "b" is -3 and 4 respectively

So, adding (-3)² => 9 and (4)² => 16 to both sides

`(x+3)^2 + (y-4)^2 = 25 + 9 + 16\\(x+3)^2 + (y-4)^2 = 50\\(x-(-3))^2 + (y-4)^2 = (5√(2)^2)`

Comparing it with
`(x-h)^2+(y-k)^2 = r^2`, where center = (h,k) and radius = r.

We get:

Center = (-3,4)

Radius =
`5√(2)`