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Section 3-3 : Circles

2. Write the equation of the circle with radius \(\sqrt 7 \) and center \(\left( { - 1, - 9} \right)\).

Show Solution

There really isn’t all that much to do with this problem. We have the radius and the center so all we need to do is plug these into the standard form of the equation from the notes.

The equation of this circle is,

\[{\left( {x - \left( { - 1} \right)} \right)^2} + {\left( {y - \left( { - 9} \right)} \right)^2} = {\left( {\sqrt 7 } \right)^2}\hspace{0.25in} \Rightarrow \hspace{0.25in}\require{bbox} \bbox[2pt,border:1px solid black]{{{{\left( {x + 1} \right)}^2} + {{\left( {y + 9} \right)}^2} = 7}}\]