If the lengths of the transverse axis and the latusrectum of a hyperbola are 6 and `(8)/(3)` respectively, then the equation of the hyperbola is . . .

Options

A. `4x^(2)-9y^(2)=72`
B. `4x^(2)-9y^(2)=36`
C. `9x^(2)-4y^(2)=72`
D. `9x^(2)-4y^(2)=36`

Answer

B

Explanation

We have,
Length of transverse axis 2a = 6`!`a = 3 and length of latusrectum ,`(2b^(2))/a=8/3`
`!2b^(2)=8/3xx3=8!b^(2)=4`
`therefore ` Required fo hyperhbola is
`(x^(2))/(a^(2)) -(y^(2))/(b^(2)) = 1 rArr (x^(2))/(9) - (y^(2))/(4) = 1 rArrr 4x^(2) - 9y^(2) = 36`