Completing the squares and comparing with an standard equation, it is found that the radius of the circle is of 4 units.
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem, the equation is:
x² + y² - 10x + 6y = -18
Then, we start the steps to complete the squares, as follows:
x² - 10x + y² + 6y = -18
(x - 5)² + (y + 3)² = -18 + 25 + 9
(x - 5)² + (y + 3)² = 16
Then, the radius is found as follows:
r² = 16 -> r = 4 units.
More can be learned about the radius of a circle at https://brainly.com/question/24307696
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