Q. 11 J5.0( 1 Vote )

In each of the fo

Answer :

Given: Foci (0, ±12), the latus-rectum = 36


To find: equation of the hyperbola


Formula used:


The standard form of the equation of the hyperbola is,



Coordinates of the foci for a standard hyperbola is given by (0, ±be)


Length of latus rectum is


According to the question:



be = 12








We know,


a2 = b2(e2 – 1)




18b = 144 – b2


b2 + 18b – 144 = 0


b2 + 24b – 6b – 144 = 0


b(b + 24) – 6(b + 24) = 0


(b + 24)(b – 6) = 0


b = -24 or b = 6


Since b is a distance, and it can’t be negative


b = 6


b2 = 36


a2 = 18b


a2 = 18(6)


b2 = 108


Hence, equation of hyperbola is:




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