Question

What are the coordinates for the center of the circle and the length of the radius

Answer 1

Given:

$x^2+y^2+14x+2y+14=0$

To find the center of the circle and the radius of the circle:

The given equation is of the form,

$x^2+y^2+2gx+2fy+c=0$

Comparing we get,

$\begin{gathered} g=7 \\ f=1 \\ c=14 \end{gathered}$

The center is,

$(-g,-f)=(-7,-1)$

The radius is,

$\begin{gathered} r=\sqrt[]{g^2+f^2-c} \\ =\sqrt[]{(7)^2+(1)^2-14} \\ =\sqrt[]{49+1-14} \\ =\sqrt[]{36} \\ =6\text{ units} \end{gathered}$

Therefore, the center of the circle is (-7,-1) and the radius of the circle is 6 units.