The equation `16 x^2-3y^2-32 x+12 y-44=0` represents a hyperbola. (a)the length of whose transvers axis is `4sqrt(3)` (b)the length of whose conjugate is `4` (c)whose center is `(-1,2)` (d)whose eccentricity is `sqrt((19)/3)`

Options

A. the length of whose transverse axis is `4sqrt(3)`
B. the length of whose conjugate axis is `4`
C. whose centre is `(-1,2)`
D. whose eccentricity is `sqrt((19)/(3))`

Answer

D

Explanation

We have,
`16(x^(2)-2x)-3(y^(2)-4y)=44`
`implies16(x-1)^(2)-3(y-2)^(2)=48`
`implies((x-1)^(2))/(3)-((y-2)^(2))/(16)=1`
This equation represents a hyperbola with eccentricity given by
`e=sqrt(1+(("Conjugate axis")/("Transverse axis")))=sqrt(1+((4)/(sqrt(3)))^(2))=sqrt((19)/(3))`