We are asked to write the equation for the circle in standard form based on the information below.
center = (-4, 1)
radius = 3
Recall that the equation of the circle in standard form is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h, k) are the coordinates of the center and r is the radius.
Substituting the coordinates of the center and value of the radius we get
[tex]\begin{gathered} (x-(-4))^2+(y-1)^2=(3)^2 \\ (x+4)^2+(y-1)^2=9 \end{gathered}[/tex]Therefore, the equation of the given circle is
[tex](x+4)^2+(y-1)^2=9[/tex]