# Math Help - Algebra II Help - Conics

1. ## Algebra II Help - Conics

I'm Having a really hard time here trying to figure out how to do these conic problems.
The directions state "Write the equation of the conic section in standard form. Then Graph the equation."

I have this booklet with the steps. We had to make it in class. I'm not totally sure i got all the steps though. I have no idea if I even did it right.
Here is the equation and all the work I've attempted on the problem. (Sorry for the bad handwriting, haha..) I circled the part where i'm really stuck.

Can someone also help me with the problem after it as well? Here is the equation:

Thanks for the help! :]

2. i)
$x^2+6x + y^2 -4 y -12 =0$
$x^2+6x + 9 - 9 + y^2 - 4y - 4 - 4 + 12 =0$
$(x+3)^2 + (y-2)^2 =1$
ii)
$y^2 - 2y + 16 -31 = y^2 -2y -15$
$y=\frac{2 \pm \sqrt{4 - (-4)15}}{2}=\frac{2 \pm 8}{2}$
Two straight lines