Hi
Note:
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)
y = (1/4)x^2, Vertex(0,0), focus(0,1) Directrix y=-1
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 )
x = (1/2)y^2 , Vertex(0,0), Focus(1/2,0): 2 = 4p, p=1/2 directrix: x = -1/2
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 )