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:  Rate this question :

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