Q. 113.8( 12 Votes )

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

Foci (0, 13), the conjugate axis is of length 24.

Answer :

Foci (0, 13), the conjugate axis is of length 24.


Here, the foci are on y-axis.


Thus,


The equation of the hyperbola is of the form


Since, the foci are (0, 13), c= 13


Since, the length of the conjugate axis is 24,


2b = 24 b = 12


We know that, a2 + b2 = c2


a2 + 122 = 132


a2 = 169 – 144 = 25


Hence, the equation of the hyperbola is


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