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Question
Find the eccentricity of the hyperbola 9y2 – 4x2 = 36.
Solution
Given equation is 9y2 – 4x2 = 36
⇒ `y^2/4 - x^2/9` = 1
Clearly it is a vertical hyperbola.
Where a = 3 and b = 2
We know that b2 = a2(e2 – 1)
⇒ 4 = 9(e2 – 1)
⇒ e2 – 1 = `4/9`
⇒ e2 = `1 + 4/9 = 13/9`
∴ e = `sqrt(13)/3`
Hence, the required value of e is `sqrt(13)/3`.
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