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

What are the coordinates for the center of the circle and the length of the radius-example-1
User Ralixyle
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1 Answer

11 votes
11 votes

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.

User Sybohy
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