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`impliesa=3`
and lenth of latusrectum, `(2b^(2))/(a)=(8)/(3)`
`implies2b^(2)=(8)/(3)xx3=8impliesb^(2)=4`
`therefore`Required equation of hyperbola is
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1implies(x^(2))/(9)-(y^(2))/(4)=1implies4x^(2)-9y^(2)=36`