Answer:
Center (3,13)
Radius r = 4
Step-by-step explanation:
Circle equation: [tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Given: [tex]y^2+x^2-6x-26y=-162[/tex]
Group x-term and y-term together:
[tex](x^2-6x) + (y^2-26y) = -162[/tex]
Complete the square for x-term, y-term using formula [tex]"x^2+(2a)x+a^2 = (x+a)^2"[/tex]
[tex](x^2-(2)(3)x+(3)^2) + (y^2-(2)(13)y+(13)^2)=-162+(3)^2+(13)^2[/tex]
[tex](x-3)^2 + (y-13)^2=16[/tex]
