Question

complete the square and write the given equation in standard form. then give the center and radius of the circle and graph the equation.
$x^{2}+y^{2}+6x + 4y+9 = 0$
the equation in standard form is $(x + 3)^{2}+(y + 2)^{2}=4$
(simplify your answer.)
the center of the circle is
(type an ordered pair.)

Explanation:

Step1: Recall the standard form of a circle equation

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Identify \(h\) and \(k\) from the given standard - form equation \((x + 3)^2+(y + 2)^2 = 4\)

We can rewrite \((x + 3)^2+(y + 2)^2 = 4\) as \((x-(-3))^2+(y-(-2))^2=2^2\).

Answer:

The center of the circle is \((-3,-2)\)