How do I convert these conics to standard form?

Question

There are two conics I need to convert from general form to standard form but I am not sure if I am going about it right. They are

$9x^2 + 5y^2 + 18x - 36 = 0$

and

$2x^2 - 8x + y + 6 = 0$

The reason that these are throwing me off is because they are both missing a part, being the $Dy$ and $By^2$ (referring to the generic general form, $Ax^2 + By^2 + Cx + Dy + E = F$).

I think that I solved the first one by just filling in $0y$ but I don't know if that is the right way to go about it. The solution I ended up with then was

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

I haven't been able to figure out the second one yet though. Any help is much appreciated!

Answer 1

Your work is correct and, yes, if a term is missed, this means that his coefficient is $0$.

For the second equation note that it is simply the parabola $ y=-2x^2+8x-6$.