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Question
The eccentricity of the hyperbola `x^2/a^2 - y^2/b^2` = 1 which passes through the points (3, 0) and `(3 sqrt(2), 2)` is ______.
Solution
The eccentricity of the hyperbola `x^2/a^2 - y^2/b^2` = 1 which passes through the points (3, 0) and `(3 sqrt(2), 2)` is e2 = `13/9`.
Explanation:
Given that the hyperbola `x^2/a^2 - y^2/b^2` = 1 is passing through the points (3, 0) and `(3 sqrt(2), 2)`
So we get a2 = 9 and b2 = 4
Again, we know that b2 = a2(e2 – 1).
This gives 4 = 9(e2 – 1)
or e2 = `13/9`
or e = `sqrt(13)/3`.
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