Respuesta :
The equation of a circle is given by:
[tex]\lparen x-h)\placeholder{⬚}^2+\left(y-k\right)^2=r^2[/tex]where (h,k) is the center and r is the radius.
In this case we know that the center of the circle is (-4,3). To find the radius we just need to remember that the radius is half the diameter, hence:
[tex]r=\frac{9}{2}[/tex]Plugging the values for the center and the radius we have that:
[tex]\begin{gathered} \lparen x-\left(-4\right))\placeholder{⬚}^2+\left(y-3\right)^2=\lparen\frac{9}{2})^2 \\ \lparen x+4)\placeholder{⬚}^2+\left(y-3\right)^2=\frac{81}{4} \end{gathered}[/tex]Therefore, the equation of the circle is:
[tex]\operatorname{\lparen}x+4)\placeholder{⬚}^2+\left(y-3\right)^2=\frac{81}{4}[/tex]