How do you graph #4x^2+4y^2+24x+32y+75=0#?

1 Answer
Alan P.
Oct 21, 2016

Draw a circle with center at #(-3,-4)# and a radius of #2 1/2# units.

Explanation:

#4x^2+4y^2+24x+32y+75=0#

#rarr 4(x^2+6xcolor(white)("XXX"))+4(y^2+8ycolor(white)("XXX"))=-75#

#rarr 4(x^2+6x+3^2)+4(y^2+8y+4^2) = -75+ 4 * (3^2) + 4 * (4^2)#

#rarr 4(x+3)^2+4(y+4)^2 = 25#

#rarr (x+3)^2+(y+4)^2=25/4 = (5/2)^2#

which is the standard form for a circle with center #(-3,-4)# and radius #5/2=2 1/2#

graph{4x^2+4y^2+24x+32y+75=0 [-7.61, 4.88, -6.81, -0.566]}

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