MHB -2.4.27 find center and radius of circle

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The discussion focuses on determining the center and radius of the circle represented by the equation x^2+y^2+6x+8y+9=0. The equation is rewritten and simplified through completing the square, resulting in the standard form (x+3)²+(y+4)²=16, indicating a center at C(-3,-4) and a radius of R=4. Participants discuss the efficiency of the completing the square method, with one expressing interest in alternative methods and potential visual representations using TikZ code. While there is acknowledgment of the possibility of other techniques, completing the square is deemed the most effective approach. The conversation highlights a focus on mathematical methods for graphing circles.
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:
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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