Question

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

Answer 1

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]}