Final answer:
To find the radius of the circle given by the equation x² + y² - 8x - 2y - 32 = 0, we need to complete the square. The equation can be rearranged and completed to the form (x - 4)² + (y - 1)² = 49. Therefore, the radius of the circle is 7.
Step-by-step explanation:
To find the radius of the circle given by the equation x² + y² - 8x - 2y - 32 = 0, we need to complete the square. Rearranging the equation, we get (x² - 8x) + (y² - 2y) = 32. Completing the square for x and y, we add 16 to both sides of the equation for the x terms and add 1 to both sides for the y terms. This gives us (x - 4)² + (y - 1)² = 49. Comparing this to the equation for a circle (x - h)² + (y - k)² = r², we can see that the center of the circle is at (4, 1) and the radius is √49, which is 7. Therefore, the radius of the circle is 7.