What is the radius of a circle whose equation is x2 y2 8x – 6y 21 = 0?

we know that

the standard form of the equation of the circle is

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem we have

Convert to standard form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

the center of the circle is

the radius of the circle is

therefore

the answer is

the radius of the circle is