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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