Putting conic section formulas in standard form

I'm having quite a bit of trouble when it comes to putting all of these into standard form and determining what specific conic section they are. Could you guys please help!?

1. Put each equation below in standard form and determine which type of conic section it is.
Depending on what type it is find the center, vertices, foci, and/or asymptotes. Use this
information to sketch the graph.
(a) x2 - 2x + 8y + 9 = 0
(b) 4x2 + y2 - 8x + 4y - 8 = 0
(c) 9x2 - y2 + 54x + 10y + 55 = 0
(d) y2 - 4x - 4 = 0
(e) y= 1/4(x2 - 2x + 5)
(f) 9x2 - 4y2 + 36x - 24y + 36 = 0
(g) 16x2 + 25y2 - 32x + 50y + 16 = 0
(h) y2 + x2 - 4x + 6y = -5


Thank you for any and all help!

Ax² +Bxy+Cy²+Dx+Ey+F=0
is used to determine the type of graph for the equations.
if B²-4AC<0 ellipse when A=C and B=0 circle
if B²-4AC =0 parabola
if B²-4AC>0 hyperbola

(a) x² - 2x + 8y + 9 = 0
A=1, B=0, C=0, D=-2, E= 8, F=9
0² -4 *1*0 =0
it is a parabola
next completing the square for the x terms
x² -2x + 1 = -8y -9 +1 = -8y -8= -8( y+1)

(x-1)² = -8(y+1)
for parabola you have

vertex (h,k)
(x-h)² = 4p(y-k) vertical axis
y=a(x-h)²+k [another form]
p>0 open up, p<0 open down,
Focus (h, k+p)
directrix y= k-p

4p =-8, p =2
p is the distance from vertex to focus, or from V to directrix

b -
use the same steps, determine what it is
you have to complete the squares for both x and y terms