Given: The equation a circle below
[tex](x-5)^2+(y+4)^2=36[/tex]To Determine: The center and the radius
Solution
The general equation a circle given the center and the radius is
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ Where \\ center=(h,k) \\ radius=r \end{gathered}[/tex]Compare the given to the general equation to get the center and radius
[tex]\begin{gathered} (x-5)^2+(y+4)^2=36 \\ (x-5)^2+(y-(-4))^2=6^2 \\ (x-h)^2+(y-k)^2=r^2 \\ h=5,k=-4,r=6 \end{gathered}[/tex]Hence, the center is (5, - 4), and radius is 6 units
