MHB -2.4.27 find center and radius of circle

karush
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Determine the graph of $x^2+y^2+6x+8y+9=0$
$\begin{array}{rll}
\textsf{rewrite} &(x^2+6x )+(y^2+8y)=-9\\
\textsf{complete square} &(x^2+6x+9)+(y^2+8y+16)=-9+9+16\\
\textsf{simplify equation} &(x+3)^2+(y+4)^2=16=4^2\\
\textsf{observation} &C(-3,-4), \quad R=4
\end{array}$

hopefully ok
is there another way to do this other than complete the square

if you are inclined to do so I would be interested in a tikz code would be fore this :unsure:
 
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this is ok

completing the square is probably the most efficient technique ...

Not saying there is no other method, but I'm not familiar with any.
 
Mahalo
often when post here an alternative is suggested...
:cool:
 
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