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Question 577691: How can someone write an equation for a hyperbola using characteristics such as the foci: (-1,9) (-1,-7) and the conjugate axis has a length of 14 units?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How can someone write an equation for a hyperbola using characteristics such as the foci: (-1,9) (-1,-7) and the conjugate axis has a length of 14 units?
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Standard form of an equation for a hyperbola with vertical transverse axis:
(y-k)^2/a^2-(x-h)^2/b^2=1, (h,k) being the (x,y) coordinates of the center.
For given hyperbola:
center:(-1,1)
given length of conjugate axis=14=2b
b=7
b^2=49
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from given foci data, c=(9+(-7))/2=16/2=8 (by midpoint formula)
c^2=64
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c^2=a^2+b^2
a^2=c^2-b^2=64-49=15
a=√15≈3.87
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equation:
(y-1)^2/15-(x+1)^2/49=1
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