Hi,
Yes, there is no y^2. This is a Parabola.
the vertex form of a parabola opening up or down, where(h,k) is the vertex.
x^2+10x+4y+9=0
(x+5)^2 -25 + 4y + 9=0
(x+5)^2 + 4y -16 =0
a = -1/4<0, open downwards, Center(-5,4) Axis of symmetry x=-5
The standard form is , where the focus is (h,k + p)
4p = -4, p = -1 , focus is (-5,3) and directrix is y = 5
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 and b are the respective vertices distances from center and ±are the foci distances from center
Standard Form of an Equation of an Hyperbola opening right and left is:
where Pt(h,k) is a center with vertices 'a' units right and left of center.
Standard Form of an Equation of an Hyperbola opening up and down is:
where Pt(h,k) is a center with vertices 'b' units up and down from center.
the vertex form of a parabola opening up or down, where(h,k) is the vertex.
The standard form is , where the focus is (h,k + p)
the vertex form of a parabola opening right or left, where(h,k) is the vertex.
The standard form is , where the focus is (h +p,k )