# Thread: Algebra II - Change this equation into Ellipse Form

1. ## Algebra II - Change this equation into Ellipse Form

So basically my teacher decided to give us only one problem for homework but its something he hasn't taught us yet...

He wants us to convert this equation:
$\displaystyle x^2+9y^2-4x+54y+49=0$

into:
$\displaystyle (x-h)^2/a^2+(y-k)^2/b^2=1$

I tried bringing the 49 to the other side and dividing everything by it but didn't know what to do from there. Please help.

2. Originally Posted by Connor
So basically my teacher decided to give us only one problem for homework but its something he hasn't taught us yet...

He wants us to convert this equation:
$\displaystyle x^2+9y^2-4x+54y+49=0$

into:
$\displaystyle (x-h)^2/a^2+(y-k)^2/b^2=1$

I tried bringing the 49 to the other side and dividing everything by it but didn't know what to do from there. Please help.
You will need to complete the square I will do the y part for you

$\displaystyle 9y^2+54y=9(y^2+6y)$

Now we take half of the coeffient on the y term and add and subtract it to give

$\displaystyle \displaystyle 9(y^2+6y)=9(y^2+6y+9-9)=9(y^2+6y+9)-81=9(y+3)^2-81$