SOLUTION: Find the equation of the hyperbola which satisfies the given condition Center (0,0), transverse axis along y-axis, passing through thepoints (5,3) and (-3,2)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation of the hyperbola which satisfies the given condition Center (0,0), transverse axis along y-axis, passing through thepoints (5,3) and (-3,2)      Log On


   

Question 894115: Find the equation of the hyperbola which satisfies the given condition Center (0,0), transverse axis along y-axis, passing through thepoints (5,3) and (-3,2)
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the equation of the hyperbola which satisfies the given condition Center (0,0), transverse axis along y-axis, passing through thepoints (5,3) and (-3,2)
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Given hyperbola has a vertical transverse axis:
Its standard form of equation:y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1
using coordinates of 2 given points, (5,3) and (-3,2)
3%5E2%2Fa%5E2-5%5E2%2Fb%5E2=1
2%5E2%2Fa%5E2-%28-3%29%5E2%2Fb%5E2=1
..
9/a^2-25/b^2=1
4/a^2-9/b^2=1
..
36/a^2-100/b^2=4
36/a^2-81/b^2=9
subtract:
-19/b^2=-5
b^2=19/5
..
81/a^2-225/b^2=9
100/=a^2-225/b^2=25
subtract:
-19/a^2=-16
a^2=19/16
equation:
y%5E2%2F%2819%2F16%29-x%5E2%2F%2819%2F5%29=1