How do you graph #x^2+y^2+x-6y+9=0#?

1 Answer
Nov 24, 2016

Answer:

Circle of radius #1/2# and centre #(-1/2,3)#

Explanation:

Complete the square for both #x# and #y#

# x^2 + y^2 + x - 6y + 9 = 0 #
# x^2 + x + y^2 - 6y = -9 #
# (x + 1/2)^2 - (1/2)^2 + (y - 3)^2 - (-3)^2 = -9 #
# (x + 1/2)^2 - 1/4 + (y - 3)^2 - 9 = -9 #
# (x + 1/2)^2 + (y - 3)^2 = 1/4 #
# (x + 1/2)^2 + (y - 3)^2 = (1/2)^2 #

So we see that it is a circle of radius #1/2# and centre #(-1/2,3)#

graph{x^2 + y^2 + x - 6y + 9 = 0 [-6, 6, -1, 5]}