The transverse axis of a hyperbola is double the conjugate axes. Whats the eccentricity of the hyperbola A) (sqrt5)/(4);B) (sqrt7)/(4);C) (7)/(4);D) (5)/(3)

Lexi Holmes

Lexi Holmes

Answered question

2023-03-26

The transverse axis of a hyperbola is double the conjugate axes. Whats the eccentricity of the hyperbola A ) 5 4 B ) 7 4 C ) 7 4 D ) 5 3

Answer & Explanation

Genesis Terrell

Genesis Terrell

Beginner2023-03-27Added 12 answers

The true answer is A

A hyperbola is given by,

Transverce axis = AB = 2a
conjugate axis = CD 2b
The relationship between these lengths and the hyperbola's eccentricity,
b 2 = a 2 ( e 2 1 ) b 2 = 4 b 2 ( e 2 1 ) i.e.  , e 2 1 = 1 4 e 2 = 5 4 e = 5 4

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