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A hyperbola has its centre at the origin...

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

B

`sqrt(3)`

C

`2/(sqrt3)`

D

`3/2`

Text Solution

Verified by Experts

The correct Answer is:
C
Let the hyperbola be `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
`2a=4 rArr a=2" or "(4, 2)" satisfies"`
`((4)^(2))/((2)^(2))-((2)^(2))/(b^(2))=1`
`4-(4)/(b^(2))=1`
`(4)/(b^(2))=3`
`b^(2)=(4)/(3)`
`b^(2)=a^(2)(e^(2)-1)`
`e^(2)=1+(b^(2))/(a^(2))=1+((4)/(3))/(4)=1+(1)/(3)" "rArr" "e=(2)/(sqrt3)`
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