Find Equation for Hyperbola or Ellipse

[realism877]

Homework Statement

6x2 + 8y2 + 32y - 16 = 0

Homework Equations

The Attempt at a Solution

I think I made a mistake.

This is how far I got

4(x-4)^+3(y+9)^=120


I made a mistake. Can someone delete this thread?

What did I do wrong?

 

[Mark44]

Homework Statement

6x2 + 8y2 + 32y - 16 = 0

Homework Equations

The Attempt at a Solution

I think I made a mistake.

This is how far I got

4(x-4)^+3(y+9)^=120


I made a mistake. Can someone delete this thread?

What did I do wrong?

I can't tell what you did wrong since you didn't show your work, but the equation you ended with isn't right.

6x² + 8y² + 32y - 16 = 0
<==> 6x² + 8y² + 32y = 16
Now complete the square in the y terms so that the equation becomes
$$\frac{x^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$$

Since there is no first-degree x term in the original equation, don't try to complete the square in the x terms.