The equation of the transvers and conjugate axes of a hyperbola are, respectively, `x+2y-3=0` and `2x-y+4=0` , and their respective lengths are `sqrt(2)` and `2sqrt(3)dot` The equation of the hyperbola is `2/5(x+2y-3)^2-3/5(2x-y+4)^2=1` `2/5(x-y-4)^2-3/5(x+2y-3)^2=1` `2(2x-y+4)^2-3(x+2y-3)^2=1` `2(x+2y-3)^2-3(2x-y+4)^2=1`

Options

A. `(2)/(5)(x+2y-3)^(2)-(3)/(5)(2x-y+4)^(2)=1`
B. `(2)/(5)(2x-y+4)^(2)-(3)/(5)(x+2y-3)^(2)=1`
C. `2(2x-y+4)^(2)-3(x+2y-3)^(2)=1`
D. `2(x+2y-3)^(2)-3(2x-y+4)^(2)=1`

Answer

B

Explanation

The equation of the hyperbola is
`({(2x-y+4)//sqrt5}^(2))/(1//2)-({(x+2y-3)//sqrt5}^(2))/(1//3)=1`
`"or "(2)/(5)(2x-y+4)^(2)-(3)/(5)(x+2y-3)^(2)=1`