How to Graph a Parabolic Equation Without a Calculator?

[Taiki_Kazuma]

What's the process that needs to take place to be able to graph the following equation (not-using a graphing calculator):
x² + 12xy + 36y² + 2x - 3y - 9 = 0

I know to use the B² - 4AC formula to identify the equation as being parabolic, though I don't understand the formula...

Looking at the equation at first, I thought you could factor it to resemble something like:
(x² = y or y² = x)

But, that's where my thinking ended (or maybe it never actually began...)


Thanks!

 

[mathman]

It's parabolic, but the axis of symmetry is not parallel to either the x or y axis,