In each of the, find the equations of the hyperbola satisfying the given conditions.

Foci (0, ), passing through (2, 3)


Foci (0, ), passing through (2, 3)


Here, the foci are on y-axis.


Thus,


The equation of the hyperbola is of the form


Since, the foci are (, 0), c =


We know that, a2 + b2 = c2


b2 = 10 – a2 …………..(1)


Since, the hyperbola passes through point (2, 3)


……………(2)


From equations (1) and (2), we get,



9(10 – a2) – 4a2 = a2(10 –a2)


90 – 9a2 – 4a2 = 10a2 – a4


a4 -23a2 + 90 = 0


a4 -18a2 -5a2+ 90 = 0


a2(a2 -18) -5(a2 -18) = 0


(a2 – 18)(a2 -5) = 0


a2 = 18 or 5


In hyperbola, c>a that is c2> a2


Thus, a2 = 5


b2 = 10 – a2 = 10 – 5 = 5


Hence, the equation of the hyperbola is


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