HELP: find the type of a conic from the given equation

Question

However, I am not sure what conic type it is.

Should it be divided by 4 in order to get a standard form of a hypebola?

Any help will be appreciated. Thank you!

Answer 1

Yes you need to divide by 4. I would factor out 2 from the y-term; it will become a 4 on the outside. This will allow you to get the correct value for $b^2$ after dividing by 4.

Answer 2

It looks like a hyperbola : $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$

It is a hyperbola with shifted origin. Replace $x\to x-h$ and $y\to y-k$ when origin is shifted to $(h,k)$