The equation of a circle is given in the form:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where (a, b) is the center of the circle and r is the radius.
The equation in the question is given to be:
[tex](x-1)^2+(y+4)^2=9[/tex]
We can rewrite it in the form given above:
[tex]\begin{gathered} 9=3^2 \\ \therefore \\ (x-1)^2+(y+4)^2=3^3 \end{gathered}[/tex]
This means that the following parameters are given for the circle:
[tex]\begin{gathered} (a,b)=(1,-4) \\ r=3 \end{gathered}[/tex]
Therefore, the radius is 3.
