Foci (± 4, 0), the latus rectum is of length 12.

Question

Philoid · Accepted Answer

Since the fonci are on x-axis, the equation of the hyperbola is of the form

= 1

Given: foci are (± 4, 0), c = 4

and length of latus rectum =  = 12

or 3x2 – y2 = 12

or c2 – a2 + b2

or 16 = a2 + 6a

or a2 + 6a – 16 = 0

or a2 + 8a – 2a – 16 = 0

or a(a + 8) – 2(a + 8) = 0

or (a + 8) (a - 2) = 0

or a = -8 or a = 2

since a cannot be negative, we take a = 2 and so b2 = 12

Therefore the equation of the required hyperbola is

= 1 ⇒ 3x2 – y2 = 12.