If the length of the latusterctum and the length of transvere axis of a hyperbola are `4sqrt(3)`and 2sqrt(3)` respectively. Then the equation of the hyperbola is

Options

A. `x^(2)/3-y^(2)/4=1`
B. `x^(2)/3-y^(2)/9=1`
C. `x^(2)/6-y^(2)/9=1`
D. `x^(2)/3-y^(2)/6=1`

Answer

D

Explanation

Given, length of latusrectum is `4sqrt3.`
` (2b^2)/(a)=4sqrt3`
` and length of transverse axis is `2sqrt3.`
` therefore 2a=2sqrt3rArra=sqrt3`
` on putting a = `sqrt3 ` in Eq. (i), we get `(2b^(2))/sqrt(3)=4 sqrt3 rArr2b^(2)=12rArrb^2 =6`
`therefore`equation of hyperbola is `(x^2)/(a^(2))-y^2/b^(2)=1rArr x^(2)/3-y^2/6=1`