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Question
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola.
`y^2/9 - x^2/27 = 1`
Solution
Equation of hyperbola: `y^2/9 - x^2/27 = 1`
The transverse axis is along the y-axis.
a2 = 9, b2 = 27
∴ c2 = a2 + b2 = 9 + 27 = 36
∴ a = 3, b = `3sqrt3`, c = 6
The coordinates of the vertices are (0, ±a) or (0, ±3)
Coordinates of foci are (0, ±c) or (0, ±6)
Eccentricity e = `c/a = 6/3 = 2`
Length of the latus rectum = `(2b^2)/a`
= `(2 xx 27)/3`
= 18
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