Question

Select the correct option from the given alternatives:

Eccentricity of the hyperbola 16x² − 3y² − 32x − 12y − 44 = 0 is

Options

• `sqrt(17/3)`

• `sqrt(19/3)`

• `sqrt(19)/3`

• `sqrt(17)/3`

Answer 1

`sqrt(19/3)`

Explanation;

16x² − 3y² − 32x − 12y − 44 = 0 

∴ 16(x − 1)² − 3(y + 2)² = 48

∴ `(x - 1)^2/3 - (y + 2)^2/16` = 1

Here, a² = 3 and b² = 16

e = `sqrt("a"^2 + "b"^2)/"a"`

= `sqrt(3 + 16)/sqrt(3)`

= `sqrt(19/3)`.