How do you find the radius of a circle with the equation x^2 + y^2 - 6x - 12y + 36 = 0?

1 Answer
Dec 16, 2015

Convert the equation to the general form for a circle
color(white)("XXX")(x-a)^2+(y-b)^2=r^2 to get the radius r=3#

Explanation:

Given:
color(white)("XXX")x^2+y^2-6x-12y+36=0

Group x and y terms separately and transfer the constant to the right side
color(white)("XXX")color(red)(x^2-6x)+color(blue)(y^2-12y)= -36

Complete each of the x and y sub-expressions as squares
color(white)("XXX")color(red)(x^2-6x+9)+color(blue)(y^2-12y+36) = -36 +color(red)(9)+color(blue)(36)

Rewrite as a sum of squared binomials equal to a square
color(white)("XXX")color(red)((x-3)^2) + color(blue)((y-6)^2) = 3^2

This is the general form of a circle with center (3,6) and radius 3
graph{x^2+y^2-6x-12y+36=0 [-3.07, 9.42, 2.885, 9.13]}