Answer: Center: (2, –4); Radius: 6.
Explanation
The equation of a circle in standard form is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h, k) is the center and r is the radius. Thus, in our given equation:
[tex]\left(x-2\right)^2+(y+4)^2=36[/tex]
• h = 2
,
• k = –4 (it is negative as negative sign times negative sign equals positive sign)
,
• r² = 36
Therefore, the center is (2, –4) and the radius is:
[tex]r^2=36[/tex][tex]\sqrt{r^2}=\sqrt{36}[/tex][tex]r=6[/tex]
