What is the radius of a circle whose equation is $x^{2}+y^{2}+8 x-6 y+21=0$ ?
2 units
3 units
4 units
5 units
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Answer
Final Answer: The radius of the circle is \(\boxed{4}\) units.
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.
