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

• Feb 20th 2011, 08:02 PM
thyrgle
Need help figuring out how to write and equation in the standard form of an ellipse.
So I have the equation:
$\displaystyle 3x^2+4y^2+8y=8$

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

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

But how can I make the right side equal 1 instead of 1/3 and not having thing multiplying by x or y?
• Feb 20th 2011, 08:51 PM
sa-ri-ga-ma
You can write the last but one step as
x^2/(4/3) + (y+1)^2 = 1
• Feb 21st 2011, 12:45 AM
skoker
you need to add on both sides. then divide. you would subtract the 4 if it was a function with no '=' sine

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

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

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