SOLUTION: Find an equation for the hyperbola that satisfies the given conditions: Vertices: (0, ±12), hyperbola passes through (−5, 18)

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Question 959130: Find an equation for the hyperbola that satisfies the given conditions: Vertices: (0, ±12), hyperbola passes through (−5, 18)
Answer by lwsshak3(11628) About Me  (Show Source):
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Find an equation for the hyperbola that satisfies the given conditions: Vertices: (0, ±12), hyperbola passes through (−5, 18)
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Given hyperbola has a vertical transverse axis
Its standard form of equation: %28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1, (h,k)=coordinates of center
For given hyperbola:
center: (0,0)
a=12
a^2=144
equation:y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1
using coordinates of given point (-5,18)
18^2/144-5^2/b^2=1
2.25-25/b^2=1
25/b^2=2.25-1=1.25=5/4
b^2=25/(5/4)=20
equation:y%5E2%2F144-x%5E2%2F20=1