How do you graph #x^2+y^2+6x-8y+9=0#?

1 Answer
Feb 12, 2016

Answer:

circle: centre(-3 , 4) and radius = 4

Explanation:

the general equation of a circle is

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

the equation here : #x^2 + y^2 + 6x - 8y + 9 = 0#
compares with the general equation and is therefore a circle.

by comparison of the 2 equations :

obtain: 2g = 6 → g = 3 , 2f = -8 → f = -4 and c = 9

centre = (-g , -f ) = (-3 , 4 )

and radius = #sqrt(g^2 + f^2 - c) = sqrt((-3)^2+4^2-9) = sqrt16 = 4#