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

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

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?

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

3. 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
$