Question

3x ^ 2 + 42x + 3y ^ 2 + 12y = 33 in standard form and what its coordinates of its center and radius? ​

Answer 1

(x +7)² +(y +2)² = 64

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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