Hi
4x^2=y^2+8y+32 =(y+4)^2 -16 + 32
4x^2-(y+4)^2 = 16
x^2/4 - (y+4)^2/16 = 1
Hyperbola:
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.
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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 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 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 )