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Find the eccetricity of hyperbola throug...

Find the eccetricity of hyperbola through `(4,2)` whose centre is `(0.0)` length of transverse axis is 4 and transverse axis along x-axis. (a) `2` (b) `sqrt3` (c) `(sqrt3)/(2)` (d) `(2)/(sqrt3)`

A

2

B

`(2)/(sqrt(3))`

C

`(3)/(2)`

D

`sqrt(3)`

Text Solution

Verified by Experts

Equation of hyperbola is given by
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
` because ` Length of transverse axis = 2a = 4
` therefore a=2`
Thus, `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` is the equation of hyperbola
` because ` It passes through (4, 2).
`therefore (16)/(4)-(4)/(b^(2))=1 rArr 4-(4)/(b^(2))=1 rArr b^(2)=(4)/(3) rArr b=(2)/(sqrt(3))`
Now, eccentricity,
`e=sqrt(1+(b^(2))/(a^(2)))=sqrt(1+((4)/(3))/(4))=sqrt(1+(1)/(3))=(2)/(sqrt(3))`
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