How do you graph 4x^2 + 4y^2 + 24x - 32y + 51?

1 Answer
Nov 9, 2015

You need to complete the square for both the x and y variables

Explanation:

4x^2 + 4y^2 + 24x - 32y + 51=0

4(x^2 + 6x) +4(y^2 - 8y) =- 51

Now, complete the squares remembering to keep the equation balanced :

4(x^2 + 6x+ 9) +4(y^2 - 8y+16) =- 51+(4)(9)+(4)(16)

4(x+3)^2 +4(y-4)^2=49

(x+3)^2 +(y-4)^2=49/4

So, this is a circle with:

Center =(-3,4)
Radius =sqrt(49/4)=3.5

Hope that helpedenter image source here