# Second derivative of the equation for an elipse.

1. Oct 3, 2012

### agent_509

1. The problem statement, all variables and given/known data
Determine the second derivative of y with respect to x when 2x2+3y2=0

2. Relevant equations
2/(3y2)
-2/(9y3)
2/(3y3)
-2/(3y2)
-2/(3y3)

3. The attempt at a solution

I took the first derivative with respect to x implicitly and came up with
-2x/3y

I then took the second derivative, but here's where I get stuck.
I wind up with:
(-2y+2x(y'))/(3y^2)

The only possible answers have only y in them, while I see no way to get rid of x in my solution. I've done this several times and come up with the same answer each time, what am I doing wrong?

2. Oct 3, 2012

### vela

Staff Emeritus
Use the equation for the ellipse to eliminate x.

3. Oct 3, 2012

### SammyS

Staff Emeritus
Did you plug your result for y' into you result for y": y" = (-2y+2x(y'))/(3y2)

4. Oct 4, 2012

### agent_509

Yes I did,but you'll notice that still doesn't get rid of x.

Vela, what do you mean by that?

5. Oct 4, 2012

### vela

Staff Emeritus
Oh, sorry, it's not an equation of an ellipse. You can use the original equation $2x^2+3y^2=0$ to solve for $x$ in terms of $y$.

6. Oct 4, 2012

### SammyS

Staff Emeritus
What did you get when you plugged your result for y' into your result for y": y" = (-2y+2x(y'))/(3y2) ?