Answer:
(x +7)² +(y +2)² = 64
Step-by-step explanation:
You want the standard form equation of the circle described by ...
3x² +42x +3y² +12y = 33
Equation of a circle
The standard form equation of a circle is ...
(x -h)² +(y -k)² = r² . . . . . . . . circle centered at (h, k) with radius r
We can make the leading coefficient 1 by dividing the given equation by 3.
x² +14x +y² +4y = 11
Completing the squares, we have ...
(x² +14x +49) +(y² +4y +4) = 11 +49 +4
(x +7)² +(y +2)² = 64
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