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

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Answer 1 · 2015-11-09T00:25:32

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

#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 helped enter image source here