Algebra II - Change this equation into Ellipse Form

**Connor** · March 21st 2011, 04:18 PM

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:
$x^2+9y^2-4x+54y+49=0$

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

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.

**TheEmptySet** · March 21st 2011, 04:28 PM

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:
$x^2+9y^2-4x+54y+49=0$

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

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

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

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

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

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