Hi,
2x^2+2y^2-8x+12y+2=0
2(x-2)^2 + 2(y+3)^2 = -2 + 8 + 18
See below descriptions of various conics
Standard Form of an Equation of a Circle is 
where Pt(h,k) is the center and r is the radius
Standard Form of an Equation of an Ellipse is 
where Pt(h,k) is the center. (a variable positioned to correspond with major axis)
a and b are the respective vertices distances from center
and ±
are the foci distances from center: a > b
Standard Form of an Equation of an Hyperbola opening up and down is:
with C(h,k) and vertices 'b' units up and down from center, 2b the length of the transverse axis
Foci 
units units up and down from center, along x = h
& Asymptotes Lines passing thru C(h,k), with slopes m = ± b/a
Standard Form of an Equation of an Hyperbola opening right and left is:
with C(h,k) and vertices 'a' units right and left of center, 2a the length of the transverse axis
Foci are units right and left of center along y = k
& Asymptotes Lines passing thru C(h,k), with slopes m = ± b/a
the vertex form of a Parabola opening up(a>0) or down(a<0), 
where(h,k) is the vertex and x = h is the Line of Symmetry
The standard form is 
, where the focus is (h,k + p)
and length of the latus rectum is 4p.
the vertex form of a Parabola opening right(a>0) or left(a<0), 
where(h,k) is the vertex and y = k is the Line of Symmetry
The standard form is 
, where the focus is (h +p,k )
and length of the latus rectum is 4p.
