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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`
Solution
`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)`.
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