Respuesta :
Given:
The equation of the circle is [tex]x^2+(y+4)^2=64[/tex]
We need to determine the center and radius of the circle.
Center:
The general form of the equation of the circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) is the center of the circle and r is the radius.
Let us compare the general form of the equation of the circle with the given equation [tex]x^2+(y+4)^2=64[/tex] to determine the center.
The given equation can be written as,
[tex](x-0)^2+(y+4)^2=64[/tex]
Comparing the two equations, we get;
(h,k) = (0,-4)
Therefore, the center of the circle is (0,-4)
Radius:
Let us compare the general form of the equation of the circle with the given equation [tex]x^2+(y+4)^2=64[/tex] to determine the radius.
Hence, the given equation can be written as,
[tex]x^2+(y+4)^2=8^2[/tex]
Comparing the two equation, we get;
[tex]r^2=8^2[/tex]
[tex]r=8[/tex]
Thus, the radius of the circle is 8
