Question 812945: Given a hyperbola with equation: (x-3)^2/25-(y+8)^2/9=1
Find the center, length of the transverse axis, slopes of the asymptotes, and tell if it is oriented left/right or up/down.
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
*****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
 opens left/right
C(3,-8) , a = 5, 2a = 10, the length of transverse axis
the slopes of the asymptotes = ±b/a = ±3/5
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 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
The standard form is  , where the focus is (h +p,k )
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