How do you write the equation of the ellipse #9x^2 + 4y^2 – 72x + 40y + 208 = 0#in standard form?

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Answer 1 · 2016-11-15T11:12:34

The standard form of the ellipse is #((x-4)^2)/2^2+((y+5)^2)/3^3=1#

Let' rewrite the equation step by step

#9x^2-72x+4y^2+40y+208=0#

#9(x^2-8x)+4(y^2+10y)=-208#

#9(x^2-8x+16)+4(y^2+10y+25)=-208+144+100#

#9(x-4)^2+4(y+5)^2=36#

Divide by #36#

#(9(x-4)^2)/36+(4(y+5)^2)/36=1#

#((x-4)^2)/4+((y+5)^2)/9=1#

graph{9x^2-72x+4y^2+40y+208=0 [-7.69, 14.82, -11.84, -0.59]}