SOLUTION: Find the equation of hyperbola whose focip(0,root 10) passing through (2,3)

Question 825770: Find the equation of hyperbola whose focip(0,root 10) passing through (2,3)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the equation of hyperbola whose focip(0,root 10) passing through (2,3)
***
hyperbola has a vertical transverse axis with center at the origin (0,0)
Its standard form of equation:
c=√10
c^2=a^2+b^2
10=a^2+b^2
b^2=10-a^2

90-9a^2-4a^2=a^2(10-a^2)
90-13a^2=10a^2-a^4
a^4-23a^2+90=0
let u=a^2
u^2-23u+90=0
(u-5)(u-18)=0
u=5=a^2
a^2=5
b^2=10-a^2=10-5
b^2=5
or
u=18=a^2
a^2=18
b^2=10-18=-8 (reject)
..
equation:

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