Question

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

Answer 1

circle: centre (-1 , -3 ) , radius = 2

Explanation:

by rewriting the equation as `x^2+y^2 +2x+6y+6 = 0`

and comparing it to the general equation of a circle:

`x^2 +y^2 +2gx + 2fy + c = 0`

by comparison : 2g = 2 →g = 1 , 2f = 6 → f = 3 and c =6

now centre = (-g , -f ) = (-1 , -3 )

and radius `= sqrt(g^2+f^2 - c ) = sqrt(1^2+3^2-6) =sqrt4 = 2`