How do you graph 4x^2 + 4y^2 + 24x + 56 = 24y?

1 Answer
Feb 9, 2016

First rearrange the terms to get all the x terms together and all the y terms together, then complete the squares to get the expression into the standard form of an ellipse or circle.

4x^2 +24x +4y^2 -24y +56 = 0
4(x^2 +6x +y^2 -6y +14)=0

We can divide the whole expression by 4 without affecting the final result.

(x+3)^2 -9 +(y-3)^2 - 9 +14=0
(x+3)^2 +(y-3)^2 -4=0
(x+3)^2 +(y-3)^2 = 4

This is now a circle with centre (-3,3) and radius 2 and can be graphed as such.