# Math Help - Determine the asymptote

1. ## Determine the asymptote

Find the asymptotes of the curve
$
x^3 + 4x^2y + 4xy^2 +5x^2+15xy+10y^2-2y+1=0
$

2. I would rearrange the equation 1st

$y^2(4x+10) +y(4x^2 +15x -2) +(x^3+5x^2+1)$

and then use the quad equation.

When you do all the algebra work you end up with

$y = \frac{-4x^2-15x+2 ^+_- \sqrt{9x^2-76x-36}}{8x+20}$

$x = \frac{-20}{8}$

$y= -\frac{x}{2} - \frac{5}{8}$

and

$9x^2 - 76x -36 \geq 0$

3. How did u get the slant asymptote could u please explain

4. since the numerator is a degree bigger than denominator it has a slant asymptote.

So use division to find out what it is

$\frac{-4x^2-15x+2}{8x-20}$