Given:
[tex]x^2+y^2+14x+2y+14=0[/tex]
To find the center of the circle and the radius of the circle:
The given equation is of the form,
[tex]x^2+y^2+2gx+2fy+c=0[/tex]
Comparing we get,
[tex]\begin{gathered} g=7 \\ f=1 \\ c=14 \end{gathered}[/tex]
The center is,
[tex](-g,-f)=(-7,-1)[/tex]
The radius is,
[tex]\begin{gathered} r=\sqrt[]{g^2+f^2-c} \\ =\sqrt[]{(7)^2+(1)^2-14} \\ =\sqrt[]{49+1-14} \\ =\sqrt[]{36} \\ =6\text{ units} \end{gathered}[/tex]
Therefore, the center of the circle is (-7,-1) and the radius of the circle is 6 units.
