A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x – axis. Then the eccentricity of the hyperbola is:
(A) 2/√3
(B) 3/2
(C) √3 (D) 2
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2/√3 is the eccentricity of the hyperbola
Step-by-step explanation:
transverse axis of length 4 along the x – axis.
along the x – axis.
=> x²/a² - y²/b² = 1
transverse axis of length 4
=> 2a = 4
=> a = 2
x²/a² - y²/b² = 1
=> x²/2² - y²/b² = 1
passes through the point (4, 2)
=> 4²/2² - 2²/b² = 1
=> 4 - 4/b² = 1
=> -4/b² = - 3
=> b² = 4/3
c² = a² + b²
=> c² = 2² + 4/3
=> c² = 4 + 4/3
=> c² = 16/3
=> c = 4/√3
eccentricity of the hyperbola c/a
= (4/√3)/2
= 2/√3
2/√3 is the eccentricity of the hyperbola
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