Question 609827: standard form for hyperbola center= (0,0) vertex= (0,6) and focus= (0,8)
Answer by ewatrrr(24785)   (Show Source):
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Hi
Note: 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.
hyperbola center= (0,0) vertex= (0,6) and focus= (0,8) ||opening up and down along the x-axis
 || focus(0,8) and 8 =  , a = ± 
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 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 )
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