Need help figuring out how to write and equation in the standard form of an ellipse.

**thyrgle** · February 20th 2011, 08:02 PM

So I have the equation:
$3x^2+4y^2+8y=8$

I'm pretty sure its an ellipse so I tried to start putting it in the standard form of an ellipse.

$3x^2+4y^2+8y=8$
$3x^2+4(y^2+2y+1)=8-4$
$3x^2+4(y+1)^2=4$
$3x^2/4+(y+1)^2=1$
$x^2/4+(y+1)^2/3=1/3$

But how can I make the right side equal 1 instead of 1/3 and not having thing multiplying by x or y?

**sa-ri-ga-ma** · February 20th 2011, 08:51 PM

You can write the last but one step as
x^2/(4/3) + (y+1)^2 = 1

**skoker** · February 21st 2011, 12:45 AM

you need to add on both sides. then divide. you would subtract the 4 if it was a function with no '=' sine

$ 3x^2+4(y^2+2y+1)=8+4 $

$ \frac{3x^2}{12}+\frac{4(y+1)^2}{12}=\frac{12}{12} $

$ \frac{x^2}{4}+\frac{(y+1)^2}{3}=1 $

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