1. ## Conic Sections

Hey guys, I need some help on Conic Sections. Specifically how to rewrite equations for hyperbola and elipses in standard form using the completeing the square method.

Here are two example problems from my math book that i have been having trouble with, i factor them using the completeting the square method but the im not sure how to get them into the standard form.

$9x^2-2y^2+18=0$
I know this one is a hyperbola.

$2x^2+2y^2-10x-18y=1$
This one is a parabola i believe.

2. 1.
$9x^2 - 2y^2 + 18 = 0$

$9x^2 - 2y^2 = -18$

$\frac{-x^2}{2} + \frac{y^2}{9} = 1$.

No need to complete the square.

2.
$2x^2 + 2y^2 - 10x - 18y = 1$

$x^2 - 5x + y^2 - 9y = \frac{1}{2}$

$x^2 - 5x + \left(-\frac{5}{2}\right)^2 + y^2 - 9y + \left(-\frac{9}{2}\right)^2 = \frac{1}{2} + \left(-\frac{5}{2}\right)^2 + \left(-\frac{9}{2}\right)^2$

$\left(x - \frac{5}{2}\right)^2 + \left(y - \frac{9}{2}\right)^2 = \frac{1}{2} + \frac{25}{4} + \frac{81}{4}$

$\left(x - \frac{5}{2}\right)^2 + \left(y - \frac{9}{2}\right)^2 = 27$

$\left(x - \frac{5}{2}\right)^2 + \left(y - \frac{9}{2}\right)^2 = \left(3\sqrt{3}\right)^2$.

So this is a circle.