Answer:
center: (-1, -4) and radius: 7
Explanation:
The standard form of the equation of a circle is given as;
[tex](x-a)^2+(y-b)^2=r^2[/tex]where (a, b) are the coordinates of the center and r is the radius.
Given the below equation of a circle in the question;
[tex](x+1)^2+(y+4)^2=49[/tex]If we compare the given equation with the standard equation of a circle, we can see that a, b and r can be found as shown below;
For a;
[tex]\begin{gathered} -a=1 \\ \therefore a=-1 \end{gathered}[/tex]For b;
[tex]\begin{gathered} -b=4 \\ b=-4 \end{gathered}[/tex]For r;
[tex]\begin{gathered} r^2=49 \\ r=\sqrt[]{49} \\ \therefore r=7 \end{gathered}[/tex]