SOLUTION: What is the length of the transverse axis of the hyperbola (x-8)^2/8^2-(y-5)^2/4^2 = 1

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Question 665079: What is the length of the transverse axis of the hyperbola (x-8)^2/8^2-(y-5)^2/4^2 = 1
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

%28x-8%29%5E2%2F8%5E2-%28y-5%29%5E2%2F4%5E2+=+1

 a = 8, length of the transverse axis(distance between the vertices) = 16

Note: Standard Form of an Equation of an Hyperbola opening right and  left is:

  %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 with C(h,k) and vertices 'a' units right and left of center,   2a the length of the transverse axis

Foci are sqrt%28a%5E2%2Bb%5E2%29 units right and left of center along y = k

& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a 



G(x) = (x - 8)^2 + 6 has the same shape as F(x) = x^2 + 6, how far to the right of F(x) is G(x) shifted? 

G(x) = (x - 8)^2 + 6  parabola V(8,6)

F(x) = x^2 + 6 parabola V(0,6)

G(x) shifted 8 units to the right