Hi,

I have been looking at quadratics of the form:

$\displaystyle ax^2 + bxy + cx^2 + dx + ey + f = 0$

From this I determined that:

$\displaystyle y = \frac{-bx - e \pm \sqrt{(b^2 - 4ac)x^2 + (2be - 4cd)x + (e^2 - 4cf)}}{2c}$

In particular I am looking at xy - 4x - 2y = 0 which is in standard form with:

a = 0, b = 1, c = 0, d = -4, e = -2, f = 0

However the above formula fails since the denominator would be 0. So I approached differently:

xy - 2y = 4x

y(x - 2) = 4x

$\displaystyle y = \frac{4x}{x - 2}$

So I used a graphing program to sketch this:

I am asked to "identify the type of graph obtained" - what sort of graph is this? I would say hyperbola but I don't think that's necessarily right?