Question 744040
Classify the conic section and write its equation in standard form. Then graph the equation.
4x^2+9y^2+40x+72y+208=0
complete the square:
4x^2+40x+9y^2+72y+208=0
4(x^2+10x+25)+9(y^2+8y+16)=-208+100+144
4(x+5)^2+9(y+4)^2=36
{{{(x+5)^2/9+(y+4)^2/4=1}}}
Given conic section is an ellipse with horizontal major axis with center at (-5,-4)
y=±(4-4(x+5)^2/9)^.5-4
see graph below as a visual check:

{{{ graph( 300, 300, -10,10, -10, 10,(4-4(x+5)^2/9)^.5-4,-(4-4(x+5)^2/9)^.5-4) }}}