SOLUTION: Find and equation for the hyperbola that satisfies the given conditions. Vertices: (0,14), (0,-14) and passes through (-5,21)

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Question 970161: Find and equation for the hyperbola that satisfies the given conditions.
Vertices: (0,14), (0,-14) and passes through (-5,21)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find and equation for the hyperbola that satisfies the given conditions.
Vertices: (0,14), (0,-14) and passes through (-5,21)
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Given hyperbola has a vertical transverse axis and center at the origin.
Its standard form of equation: y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1
a=14 (distance from center to vertices)
a^2=196
y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1
solve for b^2
plug-in coordinates of given point on the curve(-5, 21)
21%5E2%2F14%5E2-%28-5%5E2%29%2Fb%5E2=1
21%5E2%2F196-25%2Fb%5E2=1
2.25-25%2Fb%5E2=1
25/b^2=2.25-1=1.25
b^2=25/1.25
b^2=20
equation: y%5E2%2F196-x%5E2%2F20=1