Answer:
First option is the correct answer
The equation of the circle is: [tex](x-6)^2+(y-4)^2= 25[/tex]
The center is at (6, 4), and the radius is 5 units.
Step-by-step explanation:
[tex]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[/tex]
