# Math Help - Oblique Conics?

1. ## Oblique Conics?

Hi,
Is it possible to write the equation of an oblique conic in the $y=$ form?
For example, the equation $2x^2-4y^2+5xy=1$ looks like
How do I find the $y=$ version of it?

Thanks!

-Masoug

2. Not sure what you mean; looks like:
4y^2 - 5xy - 2x^2 + 1 = 0
Solve for y ?

3. Yes, how would I solve for y?

4. Treat the ' $x$' as a constant, and then substitute into the quadratic formula, or complete the square.

$4y^2 - 5xy - 2x^2 + 1 = 0$
Compare this with the general form of a quadratic:

If $ay^2+by+c=0$

then $y=\displaystyle\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, your $a=4$, $b=-5x$ and $c=-2x^2+1$, so do the substitution.