Answer:
The center is (-3,2) and the radius is r=2
Step-by-step explanation:
The general equation of the given circle is
[tex]x^2+6x+y^2-4y=-9[/tex]
Add the square of half the coefficient of the linear terms to both sides of the equation to obtain;
[tex]x^2+6x+3^2+y^2-4y+(-2)^2=-9+3^2+(-2)^2[/tex]
[tex]x^2+6x+9+y^2-4y+4=-9+9+4[/tex]
[tex]x^2+6x+9+y^2-4y+4=4[/tex]
The quadratic trinomials in x and y on the left side of the equations are perfect squares.
We factor to obtain;
[tex](x+3)^2+(y-2)^2=4[/tex]
[tex](x--3)^2+(y-2)^2=2^2[/tex]
Comparing to:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The center is (-3,2) and the radius is r=2
