Question

What’s the correct answer for this?

Answer 1

First option is the correct answer

The equation of the circle is:
`(x-6)^2+(y-4)^2= 25`

The center is at (6, 4), and the radius is 5 units.

Explanation:

`x^(2) -12x+27=-y^2 +8y\\\\x^(2) -12x+27+y^2 -8y=0\\(x^(2) -12x+36)-36+27+(y^2 -8y +16)-16=0\\(x^(2) -12x+6^2)+(y^2 -8y +4^2)-25=0\\(x-6)^2+(y-4)^2= 25\\(x-6)^2+(y-4)^2= 5^2\\Equating\: it \: with\\(x-h)^2+(y-k)^2= r^2\\we\:find:\\Center = (h,\:k) = (6,\:4)\\Radius \:(r) = 5`

Answer 2

Explanation:

Bring to one side

x^2-12x+y^2-8y+27=0

Complete the square

(x^2-12x+A)+(y^2-8y+B)=-27