SOLUTION: what is the length of the transverse axis of the hyperbola defined by the equation below (y-3)2/4 2 - (x+5)2 / 2 2=1

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Question 953443: what is the length of the transverse axis of the hyperbola defined by the equation below (y-3)2/4 2 - (x+5)2 / 2 2=1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Standard form of hyperbola with horizontal+transverse axis:
+%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1, with (h,k) being the (x,y) coordinates of the center.
Standard form of hyperbola with vertical+transverse axis:
%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1, with (h,k) being the (x,y) coordinates of the center.
The difference between these two forms is that the %28x-h%29%5E2 and %28y-k%29%5E2 terms are interchanged.
Given equation of hyperbola:
+%28y-3%29%5E2%2F4%5E+2+-+%28x%2B5%29%5E2+%2F+2%5E+2=1
This is a hyperbola of the 2nd form listed. It has a vertical transverse axis with center at (3,-5).
a%5E2=4%5E2
a=4=>distance from center to vertex
Length of transverse axis is the distance between vertices; so, =>2a=8
See the graph below for visual evidence of the algebra above: