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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.
9y2 – 4x2 = 36
Solution
Equation of hyperbola 9y2 – 4x2 = 36
Dividing by 36, `y^2/4 - x^2/9 = 1`
⇒ Transverse axis is along the x-axis.
∴ a2 = 4, b2 = 9
c2 = a2 + b2 = 4 + 9 = 13
∴ a = 2, b = 3, c = `sqrt13`
The coordinates of the vertices are (0, ±a) or (0, ±2)
The coordinates of the foci are (0, ±c) or `(0,± sqrt13)`
Eccentricity e = `c/a = sqrt13/2`
Length of the latus rectum = `(2b^2)/a`
= `(2 xx 9)/2`
= 9
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