Question 450304: What is the length of the transverse axis of the hyperbola defined by the equation below? (y-6)^2/6^2-(x+5)^2/12^2=1 Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! What is the length of the transverse axis of the hyperbola defined by the equation below
(y-6)^2/6^2-(x+5)^2/12^2=1
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Standard form of hyperbola with horizontal transverse axis: (x-h)^2/a^2-(y-k)^2/b^2=1,
with (h,k) being the (x,y) coordinates of the center.
Standard form of hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
The difference between these two forms is that the (x-h)^2 and (y-k)^2 terms are interchanged.
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Given equation of hyperbola: (y-6)^2/6^2-(x+5)^2/12^2=1
This is a hyperbola of the 2nd form listed. It has a vertical transverse axis with center at (-5,6).
a^2=6^2
a=6=distance from center to vertex
Length of transverse axis=distance between vertices=2a=12
See the graph below for visual evidence of the algebra above:
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y=(36(1+(x+5)^2/144))^.5+6
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