Q. 11 F5.0( 1 Vote )

In each of the fo

Answer :

Given: Foci and the latus-rectum = 8


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 (±ae, 0)


Length of latus rectum is


According to the question:










We know,


b2 = a2(e2 – 1)




4a = 45 – a2


a2 + 4a – 45 = 0


a2 + 9a – 5a – 45 = 0


a(a + 9) – 5(a + 9) = 0


(a + 9)(a – 5) = 0


a = -9 or a = 5


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


a = 5


a2 = 25


b2 = 4a


b2 = 4(5)


b2 = 20


Hence, equation of hyperbola is:




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