The Center of the given circle is at (-2, 3) and radius of circle is 3.
The general form of equation of a circle is;
(x - h)² + (y - k)² = r²
Where h and k are the center and r is the radius of the circle;
The given equation of the circle is;
x² + 4x + y² - 6y = -4
Add 4 to both sides to get;
x² + 4x + 4 + y² - 6y = 0
Factoring the x part gives;
(x + 2)² + y² - 6y = 0
Add 9 to both sides to get;
(x + 2)² + y² - 6y = 0
Factoring the y part gives;
(x + 2)² + (y - 3)² = 9
⇒ (x + 2)² + (y - 3)² = 3²
Comparing the above with the general circle equation form gives;
(h, k) = (-2, 3) and r = 3
Thus;
Center of circle is at (-2, 3) and radius of circle is 3.
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