Q. 11 F5.0( 1 Vote )
In each of the following find the equations of the hyperbola satisfying the given conditions
foci 
, the latus-rectum = 8
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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