SOLUTION: Find the equation of the hyperbola given that the vertices are at (0, ±4) and the foci are at (0, ±7). Show all your work.

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Question 860057: Find the equation of the hyperbola given that the vertices are at (0, ±4) and the foci are at (0, ±7). Show all your work.
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the equation of the hyperbola given that the vertices are at (0, ±4) and the foci are at (0, ±7). Show all your work.
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Given data shows hyperbola has a vertical transverse axis with center at the origin.
Its standard form of equation: y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1
a=4
a^2=16
c=7
c^2=49
c^2=a^2+b^2
b^2=c^2-a^2=49-16=33
Equation of given hyperbola: y%5E2%2F16-x%5E2%2F33=1