1. ## Conic Sections

Hi guys.

So I need help with this problem.

This is supposedly a conic
9(x-2)^2 +5(y-2)^2=-36-30y+82

I simplified it and got
9x^2 +5y^2-1=0

This is the form Ax^2 +Cy^2+Dx+Ey+F=0
I'm guessing this is an ellipse, but how do i convert this to the standard ellipse form (x^2/a^2+y^2/b^2=1)

If someone could help me, that would be great. I am seriously lost.

Thanks!

2. ## Re: Conic Sections

Originally Posted by pixel765
This is supposedly a conic
9(x-2)^2 +5(y-2)^2=-36-30y+82

I simplified it and got
9x^2 +5y^2-1=0

Thanks!
When I simplified it I got

$\displaystyle 9x^2+5y^2-36x+10y+10=0$

(I could have made a mistake but I don't think that I did)

and I think that this is what it looks like
b3e3bb9fc36b4700dc41c65050ef9918.gif

3. ## Re: Conic Sections

Originally Posted by pixel765
This is supposedly a conic
9(x-2)^2 +5(y-2)^2=-36-30y+82
I simplified it and got
9x^2 +5y^2-1=0
Warning: I did not check your algebra.

But $\displaystyle 9x^2 +5y^2=1$ is an ellipse.
In standard form it is: $\displaystyle \frac{x^2}{9^{-1}}+\frac{y^2}{5^{-1}}=1$
You can see that the center is $\displaystyle (0,0)$ and the major-axis is vertical.

4. ## Re: Conic Sections

Originally Posted by pixel765
Hi guys.

This is supposedly a conic
9(x-2)^2 +5(y-2)^2=-36-30y+82

I simplified it and got
9x^2 +5y^2-1=0

Thanks!
So, did you want the first ellipse or the second one.
If it is my error I will be seriously embarassed.