Question

an equation of a circle is x2 + y2 + 10x – 6y + 18 = 0. . . . A.Show all your work in determining the center and radius of this circle. . . B.In complete sentences, explain the procedure used.

Answer 1

A circle is a set of points in a plane equidistant from a fixed point. It has a general formula of x² + y² = r². This is if the center is at the origin. However, if the center at point h and k, the equation becomes (x-h)² + (y-k)² = r².

We write the given equation in the form (x-h)² + (y-k)² = r² by completing the square.

x² + y² + 10x – 6y + 18 = 0

(x² + 10x + 25 )+ (y² - 6y + 9) = −18 + 25 + 9 = 16
(x + 5)² + (y + 3)² = (4)²

Therefore,

center = (-5, -5)
radius = 4