Hi
What type of conic section is the following equation?
4x2 + y2 = 36
x^2/9 + y^2/36 = 1 This is an Ellipse, see below.
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)
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
