Answer:
The center is: [tex](-3, 4)[/tex] and the radius is [tex]r=2[/tex]
Step-by-step explanation:
The general equation of a circle has the following formula:
[tex](x-h)^2 + (y-k)^2 = r^2\\[/tex]
Where r is the radius of the circle and (h, k) is the center of the circle
In this case we have the following equation
[tex]x^2 + y^2 + 6x -8y +21 = 0[/tex]
To find the radius and the center of this cicunference we must rewrite the equation in the general form of a circumference completing the Square
[tex](x^2 + 6x)+ (y^2 -8y) +21 = 0\\\\(x^2 + 6x+9)+ (y^2 -8y+16) +21 = 9+16\\\\(x^2 + 6x+9)+ (y^2 -8y+16) = 9+16-21\\\\(x+3)^2+ (y-4)^2 = 4\\\\(x+3)^2+ (y-4)^2 = 2^2[/tex]
Then the center is: [tex](-3, 4)[/tex] and the radius is [tex]r=2[/tex]
