Step 1 :The equation of a circle is given by \((x-a)^2 + (y-b)^2 = r^2\), where \((a, b)\) is the center of the circle and \(r\) is the radius.
Step 2 :The given equation can be rewritten in this form by completing the square. The coefficient of \(r^2\) will give us the radius of the circle.
Step 3 :Given equation is \(x^{2}+y^{2}+8 x-6 y+21=0\)
Step 4 :By completing the square, we get \((x+4)^2 + (y-3)^2 = 4^2\)
Step 5 :From this, we can see that the radius of the circle is 4 units.
Step 6 :Final Answer: The radius of the circle is \(\boxed{4}\) units.